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2275 results in Pattern Recognition and Machine Learning

Page 23 of 114

  • 44 - Markov Decision Processes

  • Ali H. Sayed, École Polytechnique Fédérale de Lausanne
  • Book:
    Inference and Learning from Data
    Published online:
    17 March 2023
    Print publication:
    22 December 2022, pp 1807-1852

  • Summary

    Markov decision processes (MDPs) are at the core of reinforcement learning theory. Similar to Markov chains, MDPs involve an underlying Markovian process that evolves from one state to another, with the probability of visiting a new state being dependent on the most recent state. Different from Markov chains, MDPs involve both agents and actions taken by these agents. As a result, the next state is dependent on which action was chosen at the state preceding it. MDPs therefore provide a powerful framework to explore state spaces and to learn from actions and rewards.

  • 69 - Recurrent Networks

  • Ali H. Sayed, École Polytechnique Fédérale de Lausanne
  • Book:
    Inference and Learning from Data
    Published online:
    24 February 2023
    Print publication:
    22 December 2022, pp 2967-3041

  • Summary

    In the feedforward networks and convolutional neural networks (CNNs) studied in the previous chapters, the training data was assumed to be static, with no sequential relation among the samples. Using the data, we were able to train the networks to perform reliable classification tasks. There are many applications, however, where the input data will be sequential in nature, with one sample following another in some ordered manner, as happens with words in a sentence.

  • 68 - Generative Networks

  • Ali H. Sayed, École Polytechnique Fédérale de Lausanne
  • Book:
    Inference and Learning from Data
    Published online:
    24 February 2023
    Print publication:
    22 December 2022, pp 2905-2966

  • Summary

    The material in the last three chapters focused on the use of neural network structures for the solution of inference (regression and classification) problems. In this chapter, we use the same networks to develop two generative methods whose purpose is to generate samples from the same underlying distribution as the training data.

  • 50 - Least-Squares Problems

  • Ali H. Sayed, École Polytechnique Fédérale de Lausanne
  • Book:
    Inference and Learning from Data
    Published online:
    24 February 2023
    Print publication:
    22 December 2022, pp 2165-2220

  • Summary

    We studied in Chapters 29 and 30 the mean‐square error (MSE) criterion in some detail, and applied it to the problem of inferring an unknown (or hidden) variable x from the observation of another variable x when {x, y} are related by means of a linear regression model or a state‐space model.

  • 28 - Bayesian Inference

  • Ali H. Sayed, École Polytechnique Fédérale de Lausanne
  • Book:
    Inference and Learning from Data
    Published online:
    17 March 2023
    Print publication:
    22 December 2022, pp 1092-1120

  • Summary

    The mean-square-error (MSE) criterion (27.17) is one notable example of the Bayesian approach to statistical inference. In the Bayesian approach, both the unknown quantity, x, and the observation, y, are treated as random variables and an estimator x^ for x is sought by minimizing the expected value of some loss function denoted by Q(x,x^). In the previous chapter, we focused exclusively on the quadratic loss Q(x,x^)=(x−x^)2 for scalar x. In this chapter, we consider more general loss functions, which will lead to other types of inference solutions such as the mean-absolute error (MAE) and the maximum a-posteriori (MAP) estimators. We will also derive the famed Bayes classifier as a special case when the realizations for x are limited to the discrete values x∈{±1}.

  • Introduction

  • Bradley Efron, Stanford University, California
  • Book:
    Exponential Families in Theory and Practice
    Published online:
    25 November 2022
    Print publication:
    15 December 2022, pp xi-xii
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Page 23 of 114