Lecture

Maximum Entropy Modeling: Applications & Inference

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Delves into entropy in neuroscience data and ecology, exploring the representation of sensory information and the diversity of biological populations.

Quantifying Randomness and Information in Biological Data

Explores entropy, randomness, and information quantification in biological data analysis, including neuroscience and protein structure prediction.

Conditional Entropy and Information Theory Concepts

Discusses conditional entropy and its role in information theory and data compression.

Mutual Information: Continued

Explores mutual information for quantifying statistical dependence between variables and inferring probability distributions from data.

Quantifying Entropy in Neuroscience Data

Delves into quantifying entropy in neuroscience data, exploring how neuron activity represents sensory information and the implications of binary digit sequences.

Mutual Information in Biological Data

Explores mutual information in biological data, emphasizing its role in quantifying statistical dependence and analyzing protein sequences.

Random Variables and Information Theory Concepts

Introduces random variables and their significance in information theory, covering concepts like expected value and Shannon's entropy.

Introduction to Inference

Covers the basics of probability theory, random variables, joint probability, and inference.

Interpretation of Entropy

Explores the concept of entropy expressed in bits and its relation to probability distributions, focusing on information gain and loss in various scenarios.

Gaussian Naive Bayes & K-NN

Covers Gaussian Naive Bayes, K-nearest neighbors, and hyperparameter tuning in machine learning.

Unsupervised Learning: PCA & K-means

Covers unsupervised learning with PCA and K-means for dimensionality reduction and data clustering.

Random Variables and Expected Value

Introduces random variables, probability distributions, and expected values through practical examples.

Information Theory: Review and Mutual Information

Reviews information measures like entropy and introduces mutual information as a measure of information between random variables.

Probability Distributions in Environmental Studies

Explores probability distributions for random variables in air pollution and climate change studies, covering descriptive and inferential statistics.

Mutual Information: Understanding Random Variables

Explores mutual information, quantifying relationships between random variables and measuring information gain and statistical dependence.

Probability and Statistics

Delves into probability, statistics, paradoxes, and random variables, showcasing their real-world applications and properties.

Generalization Error

Explores tail bounds, information bounds, and maximal leakage in the context of generalization error.

Principal Components: Properties & Applications

Explores principal components, covariance, correlation, choice, and applications in data analysis.

Textual Data Analysis: Classification & Dimensionality Reduction

Explores textual data classification, focusing on methods like Naive Bayes and dimensionality reduction techniques like Principal Component Analysis.

Dimensionality Reduction: PCA & LDA

Covers PCA and LDA for dimensionality reduction, explaining variance maximization, eigenvector problems, and the benefits of Kernel PCA for nonlinear data.