We propose efficient Langevin Monte Carlo algorithms for sampling distributions with nonsmooth convex composite potentials, which is the sum of a continuously differentiable function and a possibly nonsmooth function. We devise such algorithms leveraging recent advances in convex analysis and optimization methods involving Bregman divergences, namely the Bregman--Moreau envelopes and the Bregman proximity operators, and in the Langevin Monte Carlo algorithms reminiscent of mirror descent. The proposed algorithms extend existing Langevin Monte Carlo algorithms in two aspects -- the ability to sample nonsmooth distributions with mirror descent-like algorithms, and the use of the more general Bregman--Moreau envelope in place of the Moreau envelope as a smooth approximation of the nonsmooth part of the potential. A particular case of the proposed scheme is reminiscent of the Bregman proximal gradient algorithm. The efficiency of the proposed methodology is illustrated with various sampling tasks at which existing Langevin Monte Carlo methods are known to perform poorly.

We study the problem of learning the structure of an optimal Bayesian network when additional constraints are posed on the network or on its moralized graph. More precisely, we consider the constraint that the network or its moralized graph are close, in terms of vertex or edge deletions, to a sparse graph class Π. For example, we show that learning an optimal network whose moralized graph has vertex deletion distance at most k from a graph with maximum degree 1 can be computed in polynomial time when k is constant. This extends previous work that gave an algorithm with such a running time for the vertex deletion distance to edgeless graphs. We then show that further extensions or improvements are presumably impossible. For example, we show that learning optimal networks where the network or its moralized graph have maximum degree 2 or connected components of size at most c, c ≥ 3, is NP-hard. Finally, we show that learning an optimal network with at most k edges in the moralized graph presumably has no f(k) · |I|O(1)-time algorithm and that, in contrast, an optimal network with at most k arcs can be computed in 2O(k) · |I|O(1) time where |I| is the total input size.

The book covers a broad array of topics not usually included in introductory machine learning texts, including supervised learning, Bayesian decision theory, parametric methods, semiparametric methods, nonparametric methods, multivariate analysis, hidden Markov models, reinforcement learning, kernel machines, graphical models, Bayesian estimation, and statistical testing. The fourth edition offers a new chapter on deep learning that discusses training, regularizing, and structuring deep neural networks such as convolutional and generative adversarial networks; new material in the chapter on reinforcement learning that covers the use of deep networks, the policy gradient methods, and deep reinforcement learning; new material in the chapter on multilayer perceptrons on autoencoders and the word2vec network; and discussion of a popular method of dimensionality reduction, t-SNE. New appendixes offer background material on linear algebra and optimization. End-of-chapter exercises help readers to apply concepts learned. Introduction to Machine Learning can be used in courses for advanced undergraduate and graduate students and as a reference for professionals.

How to sample high quality negative instances from unlabeled data, i.e., negative sampling, is important for training implicit collaborative filtering and contrastive learning models. Although previous studies have proposed some approaches to sample informative instances, few has been done to discriminating false negative from true negative for unbiased negative sampling. On the basis of our order relation analysis of negatives' scores, we first derive the class conditional density of true negatives and that of false negatives. We next design a Bayesian classifier for negative classification, from which we define a model-agnostic posterior probability estimate of an instance being true negative as a quantitative negative signal measure. We also propose a Bayesian optimal sampling rule to sample high-quality negatives. The proposed Bayesian Negative Sampling (BNS) algorithm has a linear time complexity. Experimental studies validate the superiority of BNS over the peers in terms of better sampling quality and better recommendation performance.

A major issue in the association of genes to neuroimaging phenotypes is the high dimension of both genetic data and neuroimaging data. In this article, we tackle the latter problem with an eye toward developing solutions that are relevant for disease prediction. Supported by a vast literature on the predictive power of neural networks, our proposed solution uses neural networks to extract from neuroimaging data features that are relevant for predicting Alzheimer's Disease (AD) for subsequent relation to genetics. Our neuroimaging-genetic pipeline is comprised of image processing, neuroimaging feature extraction and genetic association steps. We propose a neural network classifier for extracting neuroimaging features that are related with disease and a multivariate Bayesian group sparse regression model for genetic association. We compare the predictive power of these features to expert selected features and take a closer look at the SNPs identified with the new neuroimaging features.

Classical medium access control (MAC) protocols are interpretable, yet their task-agnostic control signaling messages (CMs) are ill-suited for emerging mission-critical applications. By contrast, neural network (NN) based protocol models (NPMs) learn to generate task-specific CMs, but their rationale and impact lack interpretability. To fill this void, in this article we propose, for the first time, a semantic protocol model (SPM) constructed by transforming an NPM into an interpretable symbolic graph written in the probabilistic logic programming language (ProbLog). This transformation is viable by extracting and merging common CMs and their connections while treating the NPM as a CM generator. By extensive simulations, we corroborate that the SPM tightly approximates its original NPM while occupying only 0.02% memory. By leveraging its interpretability and memory-efficiency, we demonstrate several SPM-enabled applications such as SPM reconfiguration for collision-avoidance, as well as comparing different SPMs via semantic entropy calculation and storing multiple SPMs to cope with non-stationary environments. Traditionally, cellular medium access control (MAC) protocols have been designed primarily for general purposes. Ko is with Inha University, Incheon, Korea (e-mail: swko@inha.ac.kr). This work has been submitted to the IEEE for possible publication. While handshaking rules and scheduling policies can partly be manipulated (e.g., grant-free access prioritization [2]), their control signaling messages (CMs) remain unchanged even when tasks and other environmental characteristics vary over time.

Bayesian hierarchical models are well-suited to analyzing the often noisy data from electroencephalography experiments in cognitive neuroscience: these models provide an intuitive framework to account for structures and correlations in the data, and they allow a straightforward handling of uncertainty. In a typical neurolinguistic experiment, event-related potentials show only very small effect sizes and frequentist approaches to data analysis fail to establish the significance of some of these effects. Here, we present a Bayesian approach to analyzing event-related potentials using as an example data from an experiment which relates word surprisal and neural response. Our model is able to estimate the effect of word surprisal on most components of the event-related potential and provides a richer description of the data. The Bayesian framework also allows easier comparison between estimates based on surprisal values calculated using different language models.

A declarative action model is a compact representation of the state transitions of dynamic systems that generalizes over world objects. The specification of declarative action models is often a complex hand-crafted task. In this paper we formulate declarative action models via state constraints, and present the learning of such models as a combinatorial search. The comprehensive framework presented here allows us to connect the learning of declarative action models to well-known problem solving tasks. In addition, our framework allows us to characterize the existing work in the literature according to four dimensions: (1) the target action models, in terms of the state transitions they define; (2) the available learning examples; (3) the functions used to guide the learning process, and to evaluate the quality of the learned action models; (4) the learning algorithm. Last, the paper lists relevant successful applications of the learning of declarative actions models and discusses some open challenges with the aim of encouraging future research work.

Unlike linear models and SVM (see Part 1), some machine learning models are really complex to learn from their mathematical formulation. Fortunately, they can be understood by following a step-by-step process they execute on a small dummy dataset. This way, you can uncover machine learning models under the hood without the "math bottleneck". You will learn three more models in this story after Part 1: K-Nearest Neighbors (KNN), Naive Bayes, and Decision Tree. KNN is a non-generalizing machine learning model since it simply "remembers" all of its train data.

This paper introduces a novel approach to embed flow-based models with hierarchical structures. The proposed framework is named Variational Flow Graphical (VFG) Model. VFGs learn the representation of high dimensional data via a message-passing scheme by integrating flow-based functions through variational inference. By leveraging the expressive power of neural networks, VFGs produce a representation of the data using a lower dimension, thus overcoming the drawbacks of many flow-based models, usually requiring a high dimensional latent space involving many trivial variables. Aggregation nodes are introduced in the VFG models to integrate forward-backward hierarchical information via a message passing scheme. Maximizing the evidence lower bound (ELBO) of data likelihood aligns the forward and backward messages in each aggregation node achieving a consistency node state. Algorithms have been developed to learn model parameters through gradient updating regarding the ELBO objective. The consistency of aggregation nodes enable VFGs to be applicable in tractable inference on graphical structures. Besides representation learning and numerical inference, VFGs provide a new approach for distribution modeling on datasets with graphical latent structures. Additionally, theoretical study shows that VFGs are universal approximators by leveraging the implicitly invertible flow-based structures. With flexible graphical structures and superior excessive power, VFGs could potentially be used to improve probabilistic inference. In the experiments, VFGs achieves improved evidence lower bound (ELBO) and likelihood values on multiple datasets.