bayesian method

Three Methods for Training on Bandit Feedback Machine Learning

There are three quite distinct ways to train a machine learning model on recommender system logs. The first method is to model the reward prediction for each possible recommendation to the user, at the scoring time the best recommendation is found by computing an argmax over the personalized recommendations. This method obeys principles such as the conditionality principle and the likelihood principle. A second method is useful when the model does not fit reality and underfits. In this case, we can use the fact that we know the distribution of historical recommendations (concentrated on previously identified good actions with some exploration) to adjust the errors in the fit to be evenly distributed over all actions. Finally, the inverse propensity score can be used to produce an estimate of the decision rules expected performance. The latter two methods violate the conditionality and likelihood principle but are shown to have good performance in certain settings. In this paper we review the literature around this fundamental, yet often overlooked choice and do some experiments using the RecoGym simulation environment.

Derivative-Free Global Optimization Algorithms: Bayesian Method and Lipschitzian Approaches Machine Learning

In this paper, we will provide an introduction to the derivative-free optimization algorithms which can be potentially applied to train deep learning models. Existing deep learning model training is mostly based on the back propagation algorithm, which updates the model variables layers by layers with the gradient descent algorithm or its variants. However, the objective functions of deep learning models to be optimized are usually non-convex and the gradient descent algorithms based on the first-order derivative can get stuck into the local optima very easily. To resolve such a problem, various local or global optimization algorithms have been proposed, which can help improve the training of deep learning models greatly. The representative examples include the Bayesian methods, Shubert-Piyavskii algorithm, Direct, LIPO, MCS, GA, SCE, DE, PSO, ES, CMA-ES, hill climbing and simulated annealing, etc. One part of these algorithms will be introduced in this paper (including the Bayesian method and Lipschitzian approaches, e.g., Shubert-Piyavskii algorithm, Direct, LIPO and MCS), and the remaining algorithms (including the population based optimization algorithms, e.g., GA, SCE, DE, PSO, ES and CMA-ES, and random search algorithms, e.g., hill climbing and simulated annealing) will be introduced in the follow-up paper [18] in detail.

15 Great Articles about Bayesian Methods and Networks


This resource is part of a series on specific topics related to data science: regression, clustering, neural networks, deep learning, decision trees, ensembles, correlation, Python, R, Tensorflow, SVM, data reduction, feature selection, experimental design, cross-validation, model fitting, and many more. To keep receiving these articles, sign up on DSC.

Bayesian Adversarial Spheres: Bayesian Inference and Adversarial Examples in a Noiseless Setting Machine Learning

Modern deep neural network models suffer from adversarial examples, i.e. confidently misclassified points in the input space. It has been shown that Bayesian neural networks are a promising approach for detecting adversarial points, but careful analysis is problematic due to the complexity of these models. Recently Gilmer et al. (2018) introduced adversarial spheres, a toy set-up that simplifies both practical and theoretical analysis of the problem. In this work, we use the adversarial sphere set-up to understand the properties of approximate Bayesian inference methods for a linear model in a noiseless setting. We compare predictions of Bayesian and non-Bayesian methods, showcasing the advantages of the former, although revealing open challenges for deep learning applications.

Learning Discrete Bayesian Networks from Continuous Data Artificial Intelligence

Learning Bayesian networks from raw data can help provide insights into the relationships between variables. While real data often contains a mixture of discrete and continuous-valued variables, many Bayesian network structure learning algorithms assume all random variables are discrete. Thus, continuous variables are often discretized when learning a Bayesian network. However, the choice of discretization policy has significant impact on the accuracy, speed, and interpretability of the resulting models. This paper introduces a principled Bayesian discretization method for continuous variables in Bayesian networks with quadratic complexity instead of the cubic complexity of other standard techniques. Empirical demonstrations show that the proposed method is superior to the established minimum description length algorithm. In addition, this paper shows how to incorporate existing methods into the structure learning process to discretize all continuous variables and simultaneously learn Bayesian network structures.

Computational Cognitive Science lab: Reading list on Bayesian methods


This list is intended to introduce some of the tools of Bayesian statistics and machine learning that can be useful to computational research in cognitive science. The first section mentions several useful general references, and the others provide supplementary readings on specific topics. If you would like to suggest some additions to the list, contact Tom Griffiths.

Frequentists Fight Back


Frequentist-leaning statisticians have numerous responses to Bayesian criticisms that may not be widely known. Broadly speaking, these rebuttals assert that Bayesian criticisms of Frequentist approaches rely on circular arguments, are self-refuting, rest mostly on semantics, or are mainly of interest to academics and irrelevant in practice. Below, I've briefly summarized the ones I'm aware of from memory and in my own words. The meaning of the term is often unclear. Is it objective Bayes, subjective Bayes, approximate Bayes, empirical Bayes, or all of the above?

Bayesian estimation for large scale multivariate Ornstein-Uhlenbeck model of brain connectivity Machine Learning

Estimation of reliable whole-brain connectivity is a crucial step towards the use of connectivity information in quantitative approaches to the study of neuropsychiatric disorders. When estimating brain connectivity a challenge is imposed by the paucity of time samples and the large dimensionality of the measurements. Bayesian estimation methods for network models offer a number of advantages in this context but are not commonly employed. Here we compare three different estimation methods for the multivariate Ornstein-Uhlenbeck model, that has recently gained some popularity for characterizing whole-brain connectivity. We first show that a Bayesian estimation of model parameters assuming uniform priors is equivalent to an application of the method of moments. Then, using synthetic data, we show that the Bayesian estimate scales poorly with number of nodes in the network as compared to an iterative Lyapunov optimization. In particular when the network size is in the order of that used for whole-brain studies (about 100 nodes) the Bayesian method needs about eight times more time samples than Lyapunov method in order to achieve similar estimation accuracy. We also show that the higher estimation accuracy of Lyapunov method is reflected in a much better classification of individuals based on the estimated connectivity from a real dataset of BOLD fMRI. Finally we show that the poor accuracy of Bayesian method is due to numerical errors, when the imaginary part of the connectivity estimate gets large compared to its real part.

Bayesian Methods for Hackers


After some recent success of Bayesian methods in machine-learning competitions, I decided to investigate the subject again. Even with my mathematical background, it took me three straight-days of reading examples and trying to put the pieces together to understand the methods. There was simply not enough literature bridging theory to practice. The problem with my misunderstanding was the disconnect between Bayesian mathematics and probabilistic programming. That being said, I suffered then so the reader would not have to now. This book attempts to bridge the gap.

Bayesian Methods for Machine Learning Coursera


About this course: Bayesian methods are used in lots of fields: from game development to drug discovery. They give superpowers to many machine learning algorithms: handling missing data, extracting much more information from small datasets. Bayesian methods also allow us to estimate uncertainty in predictions, which is a really desirable feature for fields like medicine. When Bayesian methods are applied to deep learning, it turns out that they allow you to compress your models 100 folds, and automatically tune hyperparametrs, saving your time and money. In six weeks we will discuss the basics of Bayesian methods: from how to define a probabilistic model to how to make predictions from it.