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9.675 The Development of Object and Face Recognition (MIT) 9.675 The Development of Object and Face Recognition (MIT)

Description

This course takes a 'back to the beginning' view that aims to better understand the end result. What might be the developmental processes that lead to the organization of 'booming, buzzing confusions' into coherent visual objects? This course examines key experimental results and computational proposals pertinent to the discovery of objects in complex visual inputs. The structure of the course is designed to get students to learn and to focus on the genre of study as a whole; to get a feel for how science is done in this field. This course takes a 'back to the beginning' view that aims to better understand the end result. What might be the developmental processes that lead to the organization of 'booming, buzzing confusions' into coherent visual objects? This course examines key experimental results and computational proposals pertinent to the discovery of objects in complex visual inputs. The structure of the course is designed to get students to learn and to focus on the genre of study as a whole; to get a feel for how science is done in this field.

Subjects

computational theories of human cognition | computational theories of human cognition | principles of inductive learning and inference | principles of inductive learning and inference | representation of knowledge | representation of knowledge | computational frameworks | computational frameworks | Bayesian models | Bayesian models | hierarchical Bayesian models | hierarchical Bayesian models | probabilistic graphical models | probabilistic graphical models | nonparametric statistical models | nonparametric statistical models | Bayesian Occam's razor | Bayesian Occam's razor | sampling algorithms for approximate learning and inference | sampling algorithms for approximate learning and inference | probabilistic models defined over structured representations such as first-order logic | probabilistic models defined over structured representations such as first-order logic | grammars | grammars | relational schemas | relational schemas | core aspects of cognition | core aspects of cognition | concept learning | concept learning | concept categorization | concept categorization | causal reasoning | causal reasoning | theory formation | theory formation | language acquisition | language acquisition | social inference | social inference

License

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18.441 Statistical Inference (MIT) 18.441 Statistical Inference (MIT)

Description

Reviews probability and introduces statistical inference. Point and interval estimation. The maximum likelihood method. Hypothesis testing. Likelihood-ratio tests and Bayesian methods. Nonparametric methods. Analysis of variance, regression analysis and correlation. Chi-square goodness of fit tests. More theoretical than 18.443 (Statistics for Applications) and more detailed in its treatment of statistics than 18.05 (Introduction to Probability and Statistics). Reviews probability and introduces statistical inference. Point and interval estimation. The maximum likelihood method. Hypothesis testing. Likelihood-ratio tests and Bayesian methods. Nonparametric methods. Analysis of variance, regression analysis and correlation. Chi-square goodness of fit tests. More theoretical than 18.443 (Statistics for Applications) and more detailed in its treatment of statistics than 18.05 (Introduction to Probability and Statistics).

Subjects

probability | probability | statistical inference | statistical inference | Point and interval estimation | Point and interval estimation | The maximum likelihood method | The maximum likelihood method | Hypothesis testing | Hypothesis testing | Likelihood-ratio tests | Likelihood-ratio tests | Bayesian methods | Bayesian methods | Nonparametric methods | Nonparametric methods | Analysis of variance | Analysis of variance | regression analysis | regression analysis | correlation | correlation | Chi-square goodness of fit tests | Chi-square goodness of fit tests | Likelihood-ratio tests and Bayesian methods | Likelihood-ratio tests and Bayesian methods | regression analysis and correlation | regression analysis and correlation | probability | statistical inference | probability | statistical inference | Analysis of variance | regression analysis and correlation | Analysis of variance | regression analysis and correlation

License

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6.825 Techniques in Artificial Intelligence (SMA 5504) (MIT) 6.825 Techniques in Artificial Intelligence (SMA 5504) (MIT)

Description

6.825 is a graduate-level introduction to artificial intelligence. Topics covered include: representation and inference in first-order logic, modern deterministic and decision-theoretic planning techniques, basic supervised learning methods, and Bayesian network inference and learning. This course was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5504 (Techniques in Artificial Intelligence). 6.825 is a graduate-level introduction to artificial intelligence. Topics covered include: representation and inference in first-order logic, modern deterministic and decision-theoretic planning techniques, basic supervised learning methods, and Bayesian network inference and learning. This course was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5504 (Techniques in Artificial Intelligence).

Subjects

artificial intelligence | artificial intelligence | representation | representation | inference | inference | first order logic | first order logic | deterministic planning | deterministic planning | decision-theoretic planning | decision-theoretic planning | supervised learning methods | supervised learning methods | Bayesian network inference | Bayesian network inference | learning | learning | Java | Java

License

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14.11 Putting Social Sciences to the Test: Field Experiments in Economics (MIT) 14.11 Putting Social Sciences to the Test: Field Experiments in Economics (MIT)

Description

14.11 is a new class on the topic of field (that is, 'in situ') and laboratory experiments in the social sciences - both what these experiments have taught and can teach us and how to conduct them. 14.11 is a new class on the topic of field (that is, 'in situ') and laboratory experiments in the social sciences - both what these experiments have taught and can teach us and how to conduct them.

Subjects

racial discrimination | racial discrimination | public health and persuasion | public health and persuasion | incentives | incentives | gender differences in economic environments | gender differences in economic environments | intrinsic motivation and fairness | intrinsic motivation and fairness | educational quality | educational quality | corruption | corruption | learning and social effects | learning and social effects | housing experiments | housing experiments | voting behavior and political economy | voting behavior and political economy | jury advocacy | jury advocacy | causal inference | causal inference | internal and external threats | internal and external threats | clustering | clustering | standard errors | standard errors | randomization | randomization | statistical inference with multiple outcomes | statistical inference with multiple outcomes

License

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6.438 Algorithms for Inference (MIT) 6.438 Algorithms for Inference (MIT)

Description

This is a graduate-level introduction to the principles of statistical inference with probabilistic models defined using graphical representations. The material in this course constitutes a common foundation for work in machine learning, signal processing, artificial intelligence, computer vision, control, and communication. Ultimately, the subject is about teaching you contemporary approaches to, and perspectives on, problems of statistical inference. This is a graduate-level introduction to the principles of statistical inference with probabilistic models defined using graphical representations. The material in this course constitutes a common foundation for work in machine learning, signal processing, artificial intelligence, computer vision, control, and communication. Ultimately, the subject is about teaching you contemporary approaches to, and perspectives on, problems of statistical inference.

Subjects

inference | inference | algorithm | algorithm | graphical model | graphical model | factor graph | factor graph | markov chain | markov chain | Gaussian model | Gaussian model | loopy belief propagation | loopy belief propagation | EM algorithm | EM algorithm | statistical inference | statistical inference | probabilistic graphical model | probabilistic graphical model | Hidden Markov model | Hidden Markov model | linear dynamical systems | linear dynamical systems | Sum-product algorithm | Sum-product algorithm | junction tree algorithm | junction tree algorithm | Forward-backward algorithm | Forward-backward algorithm | Kalman filtering | Kalman filtering | smoothing | smoothing | Variational method | Variational method | mean-field theory | mean-field theory | Min-sum algorithm | Min-sum algorithm | Viterbi algorithm | Viterbi algorithm | parameter estimation | parameter estimation | learning structure | learning structure

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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9.675 The Development of Object and Face Recognition (MIT)

Description

This course takes a 'back to the beginning' view that aims to better understand the end result. What might be the developmental processes that lead to the organization of 'booming, buzzing confusions' into coherent visual objects? This course examines key experimental results and computational proposals pertinent to the discovery of objects in complex visual inputs. The structure of the course is designed to get students to learn and to focus on the genre of study as a whole; to get a feel for how science is done in this field.

Subjects

computational theories of human cognition | principles of inductive learning and inference | representation of knowledge | computational frameworks | Bayesian models | hierarchical Bayesian models | probabilistic graphical models | nonparametric statistical models | Bayesian Occam's razor | sampling algorithms for approximate learning and inference | probabilistic models defined over structured representations such as first-order logic | grammars | relational schemas | core aspects of cognition | concept learning | concept categorization | causal reasoning | theory formation | language acquisition | social inference

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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15.075 Applied Statistics (MIT) 15.075 Applied Statistics (MIT)

Description

This course is an introduction to applied statistics and data analysis. Topics include collecting and exploring data, basic inference, simple and multiple linear regression, analysis of variance, nonparametric methods, and statistical computing. It is not a course in mathematical statistics, but provides a balance between statistical theory and application. Prerequisites are calculus, probability, and linear algebra. We would like to acknowledge the contributions that Prof. Roy Welsch (MIT), Prof. Gordon Kaufman (MIT), Prof. Jacqueline Telford (Johns Hopkins University), and Prof. Ramón León (University of Tennessee) have made to the course material. This course is an introduction to applied statistics and data analysis. Topics include collecting and exploring data, basic inference, simple and multiple linear regression, analysis of variance, nonparametric methods, and statistical computing. It is not a course in mathematical statistics, but provides a balance between statistical theory and application. Prerequisites are calculus, probability, and linear algebra. We would like to acknowledge the contributions that Prof. Roy Welsch (MIT), Prof. Gordon Kaufman (MIT), Prof. Jacqueline Telford (Johns Hopkins University), and Prof. Ramón León (University of Tennessee) have made to the course material.

Subjects

data analysis | data analysis | multiple regression | multiple regression | analysis of variance | analysis of variance | multivariate analysis | multivariate analysis | data mining | data mining | probability | probability | collecting data | collecting data | sampling distributions | sampling distributions | inference | inference | linear regression | linear regression | ANOVA | ANOVA | nonparametric methods | nonparametric methods | polls | polls | surveys | surveys | statistics | statistics | management science | management science | finance | finance | statistical graphics | statistical graphics | estimation | estimation | hypothesis testing | hypothesis testing | logistic regression | logistic regression | contingency tables | contingency tables | forecasting | forecasting | factor analysis | factor analysis

License

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16.410 Principles of Autonomy and Decision Making (MIT) 16.410 Principles of Autonomy and Decision Making (MIT)

Description

This course surveys a variety of reasoning, optimization, and decision-making methodologies for creating highly autonomous systems and decision support aids. The focus is on principles, algorithms, and their applications, taken from the disciplines of artificial intelligence and operations research. Reasoning paradigms include logic and deduction, heuristic and constraint-based search, model-based reasoning, planning and execution, reasoning under uncertainty, and machine learning. Optimization paradigms include linear, integer and dynamic programming. Decision-making paradigms include decision theoretic planning, and Markov decision processes. This course is offered both to undergraduate (16.410) students as a professional area undergraduate subject, in the field of aerospace information This course surveys a variety of reasoning, optimization, and decision-making methodologies for creating highly autonomous systems and decision support aids. The focus is on principles, algorithms, and their applications, taken from the disciplines of artificial intelligence and operations research. Reasoning paradigms include logic and deduction, heuristic and constraint-based search, model-based reasoning, planning and execution, reasoning under uncertainty, and machine learning. Optimization paradigms include linear, integer and dynamic programming. Decision-making paradigms include decision theoretic planning, and Markov decision processes. This course is offered both to undergraduate (16.410) students as a professional area undergraduate subject, in the field of aerospace information

Subjects

autonomy | autonomy | decision | decision | decision-making | decision-making | reasoning | reasoning | optimization | optimization | autonomous | autonomous | autonomous systems | autonomous systems | decision support | decision support | algorithms | algorithms | artificial intelligence | artificial intelligence | a.i. | a.i. | operations | operations | operations research | operations research | logic | logic | deduction | deduction | heuristic search | heuristic search | constraint-based search | constraint-based search | model-based reasoning | model-based reasoning | planning | planning | execution | execution | uncertainty | uncertainty | machine learning | machine learning | linear programming | linear programming | dynamic programming | dynamic programming | integer programming | integer programming | network optimization | network optimization | decision analysis | decision analysis | decision theoretic planning | decision theoretic planning | Markov decision process | Markov decision process | scheme | scheme | propositional logic | propositional logic | constraints | constraints | Markov processes | Markov processes | computational performance | computational performance | satisfaction | satisfaction | learning algorithms | learning algorithms | system state | system state | state | state | search treees | search treees | plan spaces | plan spaces | model theory | model theory | decision trees | decision trees | function approximators | function approximators | optimization algorithms | optimization algorithms | limitations | limitations | tradeoffs | tradeoffs | search and reasoning | search and reasoning | game tree search | game tree search | local stochastic search | local stochastic search | stochastic | stochastic | genetic algorithms | genetic algorithms | constraint satisfaction | constraint satisfaction | propositional inference | propositional inference | rule-based systems | rule-based systems | rule-based | rule-based | model-based diagnosis | model-based diagnosis | neural nets | neural nets | reinforcement learning | reinforcement learning | web-based | web-based | search trees | search trees

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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6.041 Probabilistic Systems Analysis and Applied Probability (MIT) 6.041 Probabilistic Systems Analysis and Applied Probability (MIT)

Description

This course is offered both to undergraduates (6.041) and graduates (6.431), but the assignments differ. 6.041/6.431 introduces students to the modeling, quantification, and analysis of uncertainty. Topics covered include: formulation and solution in sample space, random variables, transform techniques, simple random processes and their probability distributions, Markov processes, limit theorems, and elements of statistical inference. This course is offered both to undergraduates (6.041) and graduates (6.431), but the assignments differ. 6.041/6.431 introduces students to the modeling, quantification, and analysis of uncertainty. Topics covered include: formulation and solution in sample space, random variables, transform techniques, simple random processes and their probability distributions, Markov processes, limit theorems, and elements of statistical inference.

Subjects

probabilistic systems | probabilistic systems | probabilistic systems analysis | probabilistic systems analysis | applied probability | applied probability | uncertainty | uncertainty | uncertainty modeling | uncertainty modeling | uncertainty quantification | uncertainty quantification | analysis of uncertainty | analysis of uncertainty | uncertainty analysis | uncertainty analysis | sample space | sample space | random variables | random variables | transform techniques | transform techniques | simple random processes | simple random processes | probability distribution | probability distribution | Markov process | Markov process | limit theorem | limit theorem | statistical inference | statistical inference

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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17.869 Political Science Scope and Methods (MIT) 17.869 Political Science Scope and Methods (MIT)

Description

This course is designed to provide an introduction to a variety of empirical research methods used by political scientists. The primary aims of the course are to make you a more sophisticated consumer of diverse empirical research and to allow you to conduct sophisticated independent work in your junior and senior years. This is not a course in data analysis. Rather, it is a course on how to approach political science research. This course is designed to provide an introduction to a variety of empirical research methods used by political scientists. The primary aims of the course are to make you a more sophisticated consumer of diverse empirical research and to allow you to conduct sophisticated independent work in your junior and senior years. This is not a course in data analysis. Rather, it is a course on how to approach political science research.

Subjects

political science | political science | empirical research | empirical research | scientific method | scientific method | research design | research design | models | models | samping | samping | statistical analysis | statistical analysis | measurement | measurement | ethics | ethics | empirical | empirical | research | research | scientific | scientific | methods | methods | statistics | statistics | statistical | statistical | analysis | analysis | political | political | politics | politics | science | science | design | design | sampling | sampling | theoretical | theoretical | observation | observation | data | data | case studies | case studies | cases | cases | empirical research methods | empirical research methods | political scientists | political scientists | empirical analysis | empirical analysis | theoretical analysis | theoretical analysis | research projects | research projects | department faculty | department faculty | inference | inference | writing | writing | revision | revision | oral presentations | oral presentations | experimental method | experimental method | theories | theories | political implications | political implications

License

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6.867 Machine Learning (MIT) 6.867 Machine Learning (MIT)

Description

6.867 is an introductory course on machine learning which provides an overview of many techniques and algorithms in machine learning, beginning with topics such as simple perceptrons and ending up with more recent topics such as boosting, support vector machines, hidden Markov models, and Bayesian networks. The course gives the student the basic ideas and intuition behind modern machine learning methods as well as a bit more formal understanding of how and why they work. The underlying theme in the course is statistical inference as this provides the foundation for most of the methods covered.  6.867 is an introductory course on machine learning which provides an overview of many techniques and algorithms in machine learning, beginning with topics such as simple perceptrons and ending up with more recent topics such as boosting, support vector machines, hidden Markov models, and Bayesian networks. The course gives the student the basic ideas and intuition behind modern machine learning methods as well as a bit more formal understanding of how and why they work. The underlying theme in the course is statistical inference as this provides the foundation for most of the methods covered. 

Subjects

machine learning | machine learning | perceptrons | perceptrons | boosting | boosting | support vector machines | support vector machines | Markov | Markov | hidden Markov models | hidden Markov models | HMM | HMM | Bayesian networks | Bayesian networks | statistical inference | statistical inference | regression | regression | clustering | clustering | bias | bias | variance | variance | regularization | regularization | Generalized Linear Models | Generalized Linear Models | neural networks | neural networks | Support Vector Machine | Support Vector Machine | SVM | SVM | mixture models | mixture models | kernel density estimation | kernel density estimation | gradient descent | gradient descent | quadratic programming | quadratic programming | EM algorithm | EM algorithm | orward-backward algorithm | orward-backward algorithm | junction tree algorithm | junction tree algorithm | Gibbs sampling | Gibbs sampling

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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6.050J Information and Entropy (MIT) 6.050J Information and Entropy (MIT)

Description

6.050J / 2.110J presents the unified theory of information with applications to computing, communications, thermodynamics, and other sciences. It covers digital signals and streams, codes, compression, noise, and probability, reversible and irreversible operations, information in biological systems, channel capacity, maximum-entropy formalism, thermodynamic equilibrium, temperature, the Second Law of Thermodynamics, and quantum computation. Designed for MIT freshmen as an elective, this course has been jointly developed by MIT's Departments of Electrical Engineering and Computer Science and Mechanical Engineering. There is no known course similar to 6.050J / 2.110J offered at any other university.  6.050J / 2.110J presents the unified theory of information with applications to computing, communications, thermodynamics, and other sciences. It covers digital signals and streams, codes, compression, noise, and probability, reversible and irreversible operations, information in biological systems, channel capacity, maximum-entropy formalism, thermodynamic equilibrium, temperature, the Second Law of Thermodynamics, and quantum computation. Designed for MIT freshmen as an elective, this course has been jointly developed by MIT's Departments of Electrical Engineering and Computer Science and Mechanical Engineering. There is no known course similar to 6.050J / 2.110J offered at any other university. 

Subjects

information and entropy | information and entropy | computing | computing | communications | communications | thermodynamics | thermodynamics | digital signals and streams | digital signals and streams | codes | codes | compression | compression | noise | noise | probability | probability | reversible operations | reversible operations | irreversible operations | irreversible operations | information in biological systems | information in biological systems | channel capacity | channel capacity | aximum-entropy formalism | aximum-entropy formalism | thermodynamic equilibrium | thermodynamic equilibrium | temperature | temperature | second law of thermodynamics quantum computation | second law of thermodynamics quantum computation | maximum-entropy formalism | maximum-entropy formalism | second law of thermodynamics | second law of thermodynamics | quantum computation | quantum computation | biological systems | biological systems | unified theory of information | unified theory of information | digital signals | digital signals | digital streams | digital streams | bits | bits | errors | errors | processes | processes | inference | inference | maximum entropy | maximum entropy | physical systems | physical systems | energy | energy | quantum information | quantum information | 6.050 | 6.050 | 2.110 | 2.110

License

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16.410 Principles of Autonomy and Decision Making (MIT) 16.410 Principles of Autonomy and Decision Making (MIT)

Description

This course surveys a variety of reasoning, optimization, and decision-making methodologies for creating highly autonomous systems and decision support aids. The focus is on principles, algorithms, and their applications, taken from the disciplines of artificial intelligence and operations research. Reasoning paradigms include logic and deduction, heuristic and constraint-based search, model-based reasoning, planning and execution, reasoning under uncertainty, and machine learning. Optimization paradigms include linear, integer and dynamic programming. Decision-making paradigms include decision theoretic planning, and Markov decision processes. This course is offered both to undergraduate (16.410) students as a professional area undergraduate subject, in the field of aerospace information This course surveys a variety of reasoning, optimization, and decision-making methodologies for creating highly autonomous systems and decision support aids. The focus is on principles, algorithms, and their applications, taken from the disciplines of artificial intelligence and operations research. Reasoning paradigms include logic and deduction, heuristic and constraint-based search, model-based reasoning, planning and execution, reasoning under uncertainty, and machine learning. Optimization paradigms include linear, integer and dynamic programming. Decision-making paradigms include decision theoretic planning, and Markov decision processes. This course is offered both to undergraduate (16.410) students as a professional area undergraduate subject, in the field of aerospace information

Subjects

autonomy | autonomy | decision | decision | decision-making | decision-making | reasoning | reasoning | optimization | optimization | autonomous | autonomous | autonomous systems | autonomous systems | decision support | decision support | algorithms | algorithms | artificial intelligence | artificial intelligence | a.i. | a.i. | operations | operations | operations research | operations research | logic | logic | deduction | deduction | heuristic search | heuristic search | constraint-based search | constraint-based search | model-based reasoning | model-based reasoning | planning | planning | execution | execution | uncertainty | uncertainty | machine learning | machine learning | linear programming | linear programming | dynamic programming | dynamic programming | integer programming | integer programming | network optimization | network optimization | decision analysis | decision analysis | decision theoretic planning | decision theoretic planning | Markov decision process | Markov decision process | scheme | scheme | propositional logic | propositional logic | constraints | constraints | Markov processes | Markov processes | computational performance | computational performance | satisfaction | satisfaction | learning algorithms | learning algorithms | system state | system state | state | state | search treees | search treees | plan spaces | plan spaces | model theory | model theory | decision trees | decision trees | function approximators | function approximators | optimization algorithms | optimization algorithms | limitations | limitations | tradeoffs | tradeoffs | search and reasoning | search and reasoning | game tree search | game tree search | local stochastic search | local stochastic search | stochastic | stochastic | genetic algorithms | genetic algorithms | constraint satisfaction | constraint satisfaction | propositional inference | propositional inference | rule-based systems | rule-based systems | rule-based | rule-based | model-based diagnosis | model-based diagnosis | neural nets | neural nets | reinforcement learning | reinforcement learning | web-based | web-based | search trees | search trees

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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12.864 Inference from Data and Models (MIT) 12.864 Inference from Data and Models (MIT)

Description

The course is directed at making scientifically sensible deductions from the combination of observations with dynamics and kinematics represented, generically, as "models". There are two overlapping central themeslinear "inverse" methods and data "assimilation" including regression, singular value decomposition, objective mapping, non-stationary models and data, Kalman filters, adjoint methods ("assimilation") etc.standard time series analysis, including basic statistics, Fourier methods, spectra, coherence, filtering, etc. The course is directed at making scientifically sensible deductions from the combination of observations with dynamics and kinematics represented, generically, as "models". There are two overlapping central themeslinear "inverse" methods and data "assimilation" including regression, singular value decomposition, objective mapping, non-stationary models and data, Kalman filters, adjoint methods ("assimilation") etc.standard time series analysis, including basic statistics, Fourier methods, spectra, coherence, filtering, etc.

Subjects

observation | observation | kinematical models | kinematical models | dynamical models | dynamical models | basic statistics | basic statistics | linear algebra | linear algebra | inverse methods | inverse methods | singular value decompositions | singular value decompositions | control theory | control theory | sequential estimation | sequential estimation | Kalman filters | Kalman filters | smoothing algorithms | smoothing algorithms | adjoint/Pontryagin principle methods | adjoint/Pontryagin principle methods | model testing | model testing | stationary processes | stationary processes | Fourier methods | Fourier methods | z-transforms | z-transforms | sampling theorems | sampling theorems | spectra | spectra | multi-taper methods | multi-taper methods | coherences | coherences | filtering | filtering | quantitative combinations | quantitative combinations | realistic observations | realistic observations | data assimilations | data assimilations | deduction | deduction | regression | regression | objective mapping | objective mapping | time series analysis | time series analysis | inference | inference

License

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6.041 Probabilistic Systems Analysis and Applied Probability (MIT) 6.041 Probabilistic Systems Analysis and Applied Probability (MIT)

Description

This course is offered both to undergraduates (6.041) and graduates (6.431), but the assignments differ. 6.041/6.431 introduces students to the modeling, quantification, and analysis of uncertainty. Topics covered include: formulation and solution in sample space, random variables, transform techniques, simple random processes and their probability distributions, Markov processes, limit theorems, and elements of statistical inference. This course is offered both to undergraduates (6.041) and graduates (6.431), but the assignments differ. 6.041/6.431 introduces students to the modeling, quantification, and analysis of uncertainty. Topics covered include: formulation and solution in sample space, random variables, transform techniques, simple random processes and their probability distributions, Markov processes, limit theorems, and elements of statistical inference.

Subjects

probabilistic systems | probabilistic systems | probabilistic systems analysis | probabilistic systems analysis | applied probability | applied probability | uncertainty | uncertainty | uncertainty modeling | uncertainty modeling | uncertainty quantification | uncertainty quantification | analysis of uncertainty | analysis of uncertainty | uncertainty analysis | uncertainty analysis | sample space | sample space | random variables | random variables | transform techniques | transform techniques | simple random processes | simple random processes | probability distribution | probability distribution | Markov process | Markov process | limit theorem | limit theorem | statistical inference | statistical inference

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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17.878 Qualitative Research: Design and Methods (MIT) 17.878 Qualitative Research: Design and Methods (MIT)

Description

This seminar explores the development and application of qualitative research designs and methods in political analysis. It considers a broad array of approaches, from exploratory narratives to focused-comparison case studies, for investigating plausible alternative hypotheses. The focus is on analysis, not data collection. This seminar explores the development and application of qualitative research designs and methods in political analysis. It considers a broad array of approaches, from exploratory narratives to focused-comparison case studies, for investigating plausible alternative hypotheses. The focus is on analysis, not data collection.

Subjects

development and application of qualitative research designs and methods in political analysis | development and application of qualitative research designs and methods in political analysis | exploratory narrative | exploratory narrative | focused-comparison case studies | focused-comparison case studies | investigating plausible alternative hypotheses | investigating plausible alternative hypotheses | research methods | research methods | methodology | methodology | rival hypothesis | rival hypothesis | research designs | research designs | plausibility | plausibility | political analysis | political analysis | data analysis | data analysis | validity | validity | reliability | reliability | inference | inference | observations | observations | cases | cases | subjects | subjects | research agenda | research agenda | qualitative methods | qualitative methods | qualitative research | qualitative research

License

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17.432 Causes of War: Theory and Method (MIT) 17.432 Causes of War: Theory and Method (MIT)

Description

This course explores the causes of modern war with a focus on preventable causes. Course readings cover theoretical, historical, and methodological topics. Major theories of war are explored and assessed in the first few weeks of the class, asking at each stage "are these good theories?" and "how could they be tested?" Basic social scientific inference -- what are theories? What are good theories? How should theories be framed and tested? -- and case study methodology are also discussed. The second half of the course explores the history of the outbreak of some major wars. We use these cases as raw material for case studies, asking "if these episodes were the subject of case studies, how should those studies be performed, and what could be learned from them?" This course explores the causes of modern war with a focus on preventable causes. Course readings cover theoretical, historical, and methodological topics. Major theories of war are explored and assessed in the first few weeks of the class, asking at each stage "are these good theories?" and "how could they be tested?" Basic social scientific inference -- what are theories? What are good theories? How should theories be framed and tested? -- and case study methodology are also discussed. The second half of the course explores the history of the outbreak of some major wars. We use these cases as raw material for case studies, asking "if these episodes were the subject of case studies, how should those studies be performed, and what could be learned from them?"

Subjects

Political science | Political science | security studies | security studies | war | war | preventable causes | preventable causes | theoretical | theoretical | historical | historical | methodological | methodological | topics | topics | social scientific inference | social scientific inference | history | history | outbreak | outbreak | causes | causes | method. | method. | method | method

License

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17.872 Quantitative Research in Political Science and Public Policy (MIT) 17.872 Quantitative Research in Political Science and Public Policy (MIT)

Description

This course provides students with a rigorous introduction to Statistics for Political Science. Topics include basic mathematical tools used in social science modeling and statistics, probability theory, theory of estimation and inference, and statistical methods, especially differences of means and regression. The course is often taken by students outside of political science, especially those in business, urban studies, and various fields of public policy, such as public health. Examples draw heavily from political science, but some problems come from other areas, such as labor economics. This course provides students with a rigorous introduction to Statistics for Political Science. Topics include basic mathematical tools used in social science modeling and statistics, probability theory, theory of estimation and inference, and statistical methods, especially differences of means and regression. The course is often taken by students outside of political science, especially those in business, urban studies, and various fields of public policy, such as public health. Examples draw heavily from political science, but some problems come from other areas, such as labor economics.

Subjects

mathematical economics | mathematical economics | quatitative research | quatitative research | political science | political science | public policy | public policy | modeling | modeling | probability theory | probability theory | estimation | estimation | inference | inference | analytical methods | analytical methods | regression | regression | statistical means | statistical means | labor | labor | public health | public health

License

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6.041 Probabilistic Systems Analysis and Applied Probability (MIT) 6.041 Probabilistic Systems Analysis and Applied Probability (MIT)

Description

Includes audio/video content: AV lectures. Welcome to 6.041/6.431, a subject on the modeling and analysis of random phenomena and processes, including the basics of statistical inference. Nowadays, there is broad consensus that the ability to think probabilistically is a fundamental component of scientific literacy. For example: The concept of statistical significance (to be touched upon at the end of this course) is considered by the Financial Times as one of "The Ten Things Everyone Should Know About Science". A recent Scientific American article argues that statistical literacy is crucial in making health-related decisions. Finally, an article in the New York Times identifies statistical data analysis as an upcoming profession, valuable everywhere, from Google and Includes audio/video content: AV lectures. Welcome to 6.041/6.431, a subject on the modeling and analysis of random phenomena and processes, including the basics of statistical inference. Nowadays, there is broad consensus that the ability to think probabilistically is a fundamental component of scientific literacy. For example: The concept of statistical significance (to be touched upon at the end of this course) is considered by the Financial Times as one of "The Ten Things Everyone Should Know About Science". A recent Scientific American article argues that statistical literacy is crucial in making health-related decisions. Finally, an article in the New York Times identifies statistical data analysis as an upcoming profession, valuable everywhere, from Google and

Subjects

probability | probability | probability models | probability models | bayes rule | bayes rule | discrete random variables | discrete random variables | continuous random variables | continuous random variables | bernoulli process | bernoulli process | poisson process | poisson process | markov chains | markov chains | central limit theorem | central limit theorem | statistical inference | statistical inference

License

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6.034 Artificial Intelligence (MIT) 6.034 Artificial Intelligence (MIT)

Description

Includes audio/video content: AV lectures. This course introduces students to the basic knowledge representation, problem solving, and learning methods of artificial intelligence. Upon completion of 6.034, students should be able to develop intelligent systems by assembling solutions to concrete computational problems; understand the role of knowledge representation, problem solving, and learning in intelligent-system engineering; and appreciate the role of problem solving, vision, and language in understanding human intelligence from a computational perspective. Includes audio/video content: AV lectures. This course introduces students to the basic knowledge representation, problem solving, and learning methods of artificial intelligence. Upon completion of 6.034, students should be able to develop intelligent systems by assembling solutions to concrete computational problems; understand the role of knowledge representation, problem solving, and learning in intelligent-system engineering; and appreciate the role of problem solving, vision, and language in understanding human intelligence from a computational perspective.

Subjects

artificial intelligence | artificial intelligence | knowledge representation | knowledge representation | problem solving | problem solving | learning methods | learning methods | intelligent systems | intelligent systems | basic search | basic search | optimal search | optimal search | neural nets | neural nets | genetic algorithms | genetic algorithms | support vector machines | support vector machines | boosting | boosting | probabilistic inference | probabilistic inference

License

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6.867 Machine Learning (MIT) 6.867 Machine Learning (MIT)

Description

6.867 is an introductory course on machine learning which gives an overview of many concepts, techniques, and algorithms in machine learning, beginning with topics such as classification and linear regression and ending up with more recent topics such as boosting, support vector machines, hidden Markov models, and Bayesian networks. The course will give the student the basic ideas and intuition behind modern machine learning methods as well as a bit more formal understanding of how, why, and when they work. The underlying theme in the course is statistical inference as it provides the foundation for most of the methods covered. 6.867 is an introductory course on machine learning which gives an overview of many concepts, techniques, and algorithms in machine learning, beginning with topics such as classification and linear regression and ending up with more recent topics such as boosting, support vector machines, hidden Markov models, and Bayesian networks. The course will give the student the basic ideas and intuition behind modern machine learning methods as well as a bit more formal understanding of how, why, and when they work. The underlying theme in the course is statistical inference as it provides the foundation for most of the methods covered.

Subjects

machine learning algorithms | machine learning algorithms | statistical inference | statistical inference | representation | representation | generalization | generalization | model selection | model selection | linear/additive models | linear/additive models | active learning | active learning | boosting | boosting | support vector machines | support vector machines | hidden Markov models | hidden Markov models | Bayesian networks | Bayesian networks | classification | classification | linear regression | linear regression | modern machine learning methods | modern machine learning methods

License

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6.041 Probabilistic Systems Analysis and Applied Probability (MIT) 6.041 Probabilistic Systems Analysis and Applied Probability (MIT)

Description

This course is offered both to undergraduates (6.041) and graduates (6.431), but the assignments differ. 6.041/6.431 introduces students to the modeling, quantification, and analysis of uncertainty. Topics covered include: formulation and solution in sample space, random variables, transform techniques, simple random processes and their probability distributions, Markov processes, limit theorems, and elements of statistical inference. This course is offered both to undergraduates (6.041) and graduates (6.431), but the assignments differ. 6.041/6.431 introduces students to the modeling, quantification, and analysis of uncertainty. Topics covered include: formulation and solution in sample space, random variables, transform techniques, simple random processes and their probability distributions, Markov processes, limit theorems, and elements of statistical inference.

Subjects

probabilistic systems | probabilistic systems | probabilistic systems analysis | probabilistic systems analysis | applied probability | applied probability | uncertainty | uncertainty | uncertainty modeling | uncertainty modeling | uncertainty quantification | uncertainty quantification | analysis of uncertainty | analysis of uncertainty | uncertainty analysis | uncertainty analysis | sample space | sample space | random variables | random variables | transform techniques | transform techniques | simple random processes | simple random processes | probability distribution | probability distribution | Markov process | Markov process | limit theorem | limit theorem | statistical inference | statistical inference

License

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6.883 Program Analysis (MIT) 6.883 Program Analysis (MIT)

Description

6.883 is a graduate seminar that investigates a variety of program analysis techniques that address software engineering tasks. Static analysis topics include abstract interpretation (dataflow), type systems, model checking, decision procedures (SAT, BDDs), theorem-proving. Dynamic analysis topics include testing, fault isolation (debugging), model inference, and visualization. While the course focuses on the design and implementation of programming tools, the material will be useful to anyone who wishes to improve his or her programming or understand the state of the art. Students are expected to read classic and current technical papers, actively participate in class discussion, perform small exercises that provide experience with a variety of tools, and complete a team research project. 6.883 is a graduate seminar that investigates a variety of program analysis techniques that address software engineering tasks. Static analysis topics include abstract interpretation (dataflow), type systems, model checking, decision procedures (SAT, BDDs), theorem-proving. Dynamic analysis topics include testing, fault isolation (debugging), model inference, and visualization. While the course focuses on the design and implementation of programming tools, the material will be useful to anyone who wishes to improve his or her programming or understand the state of the art. Students are expected to read classic and current technical papers, actively participate in class discussion, perform small exercises that provide experience with a variety of tools, and complete a team research project.

Subjects

program analysis | program analysis | static analysis | static analysis | abstract interpretation (dataflow) | abstract interpretation (dataflow) | type systems | type systems | model checking | model checking | decision procedures (SAT | decision procedures (SAT | BDDs) | BDDs) | theorem-proving | theorem-proving | dynamic analysis | dynamic analysis | testing | testing | fault isolation (debugging) | fault isolation (debugging) | model inference | and visualization | model inference | and visualization | decision procedures (SAT | BDDs) | decision procedures (SAT | BDDs)

License

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6.821 Programming Languages (MIT) 6.821 Programming Languages (MIT)

Description

6.821 teaches the principles of functional, imperative, and logic programming languages. Topics covered include: meta-circular interpreters, semantics (operational and denotational), type systems (polymorphism, inference, and abstract types), object oriented programming, modules, and multiprocessing. The course involves substantial programming assignments and problem sets as well as a significant amount of reading. The course uses the Scheme+ programming language for all of its assignments. 6.821 teaches the principles of functional, imperative, and logic programming languages. Topics covered include: meta-circular interpreters, semantics (operational and denotational), type systems (polymorphism, inference, and abstract types), object oriented programming, modules, and multiprocessing. The course involves substantial programming assignments and problem sets as well as a significant amount of reading. The course uses the Scheme+ programming language for all of its assignments.

Subjects

Scheme | Scheme | Scheme+ | Scheme+ | programming | programming | programming language | programming language | functional programming language | functional programming language | imperative programming language | imperative programming language | ogic programming languages | ogic programming languages | meta-circular interpreters | meta-circular interpreters | operational semantics | operational semantics | denotational semantics | denotational semantics | type systems | type systems | polymorphism | polymorphism | inference | inference | abstract types | abstract types | object oriented programming | object oriented programming | modules | modules | multiprocessing | multiprocessing

License

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9.69 Foundations of Cognition (MIT) 9.69 Foundations of Cognition (MIT)

Description

Advances in cognitive science have resolved, clarified, and sometimes complicated some of the great questions of Western philosophy: what is the structure of the world and how do we come to know it; does everyone represent the world the same way; what is the best way for us to act in the world. Specific topics include color, objects, number, categories, similarity, inductive inference, space, time, causality, reasoning, decision-making, morality and consciousness. Readings and discussion include a brief philosophical history of each topic and focus on advances in cognitive and developmental psychology, computation, neuroscience, and related fields. At least one subject in cognitive science, psychology, philosophy, linguistics, or artificial intelligence is required. An additional project i Advances in cognitive science have resolved, clarified, and sometimes complicated some of the great questions of Western philosophy: what is the structure of the world and how do we come to know it; does everyone represent the world the same way; what is the best way for us to act in the world. Specific topics include color, objects, number, categories, similarity, inductive inference, space, time, causality, reasoning, decision-making, morality and consciousness. Readings and discussion include a brief philosophical history of each topic and focus on advances in cognitive and developmental psychology, computation, neuroscience, and related fields. At least one subject in cognitive science, psychology, philosophy, linguistics, or artificial intelligence is required. An additional project i

Subjects

cognitive science | cognitive science | Western philosophy | Western philosophy | structure | structure | color | color | objects | objects | number | number | similarity | similarity | inductive inference | inductive inference | space | space | time | time | reasoning | reasoning | decision-making | decision-making | morality | morality | consciousness | consciousness | development | development | psychology | psychology | computation | computation | neuroscience | neuroscience | philosophy | philosophy | linguistics | linguistics | artificial intelligence | artificial intelligence

License

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