Machine Learning (ML) is one of the most exciting and dynamic areas of modern research and application. The purpose of this review is to provide an introduction to the core concepts and tools of machine learning in a manner easily understood and intuitive to physicists. The review begins by covering fundamental concepts in ML and modern statistics such as the bias-variance tradeoff, overfitting, regularization, and generalization before moving on to more advanced topics in both supervised and unsupervised learning. Topics covered in the review include ensemble models, deep learning and neural networks, clustering and data visualization, energy-based models (including MaxEnt models and Restricted Boltzmann Machines), and variational methods. Throughout, we emphasize the many natural connections between ML and statistical physics. A notable aspect of the review is the use of Python notebooks to introduce modern ML/statistical packages to readers using physics-inspired datasets (the Ising Model and Monte-Carlo simulations of supersymmetric decays of proton-proton collisions). We conclude with an extended outlook discussing possible uses of machine learning for furthering our understanding of the physical world as well as open problems in ML where physicists maybe able to contribute. (Notebooks are available at https://physics.bu.edu/~pankajm/MLnotebooks.html )

A broad spectrum of data from different modalities are generated in the healthcare domain every day, including scalar data (e.g., clinical measures collected at hospitals), tensor data (e.g., neuroimages analyzed by research institutes), graph data (e.g., brain connectivity networks), and sequence data (e.g., digital footprints recorded on smart sensors). Capability for modeling information from these heterogeneous data sources is potentially transformative for investigating disease mechanisms and for informing therapeutic interventions. Our works in this thesis attempt to facilitate healthcare applications in the setting of broad learning which focuses on fusing heterogeneous data sources for a variety of synergistic knowledge discovery and machine learning tasks. We are generally interested in computer-aided diagnosis, precision medicine, and mobile health by creating accurate user profiles which include important biomarkers, brain connectivity patterns, and latent representations. In particular, our works involve four different data mining problems with application to the healthcare domain: multi-view feature selection, subgraph pattern mining, brain network embedding, and multi-view sequence prediction.

How real is this relationship? This is a ubiquitous question that presents itself not only in judging interpersonal connections but also in evaluating correlations and causality throughout science and engineering. Two reasons for reaching incorrect conclusions based on observed relationships in collected data are chance and outside influences. For example, we can flip two coins that both show heads, or observe that today's temperature measurements on the west coast of the continental USA seem to correlate with tomorrow's on the east coast throughout the year. In the first case, we might not immediately conclude that coins are related, since the number of flips we observe is not very large relative to the possible variance of the process, and the apparent link we observed is up to chance. In the second case, we still may hesitate to use west coast weather to understand and predict east coast weather, since in reality both are closely following a seasonal trend. Establishing interpretable relationships between entities while mitigating the effects of chance can be achieved via sparse optimization methods, such as regression (Lasso) [1] and inverse covariance estimation [2]. In addition, the extension to time series via vector autoregression [3], [4] yields interpretations related to Granger causality [5]. In each of these settings, estimated nonzero values correspond to actual relations, while zeros correspond to absence of relations.

An important preprocessing step in most data analysis pipelines aims to extract a small set of sources that explain most of the data. Currently used algorithms for blind source separation (BSS), however, often fail to extract the desired sources and need extensive cross-validation. In contrast, their rarely used probabilistic counterparts can get away with little cross-validation and are more accurate and reliable but no simple and scalable implementations are available. Here we present a novel probabilistic BSS framework (DECOMPOSE) that can be flexibly adjusted to the data, is extensible and easy to use, adapts to individual sources and handles large-scale data through algorithmic efficiency. DECOMPOSE encompasses and generalises many traditional BSS algorithms such as PCA, ICA and NMF and we demonstrate substantial improvements in accuracy and robustness on artificial and real data.

We propose a Bayesian optimization algorithm for objective functions that are sums or integrals of expensive-to-evaluate functions, allowing noisy evaluations. These objective functions arise in multi-task Bayesian optimization for tuning machine learning hyperparameters, optimization via simulation, and sequential design of experiments with random environmental conditions. Our method is average-case optimal by construction when a single evaluation of the integrand remains within our evaluation budget. Achieving this one-step optimality requires solving a challenging value of information optimization problem, for which we provide a novel efficient discretization-free computational method. We also provide consistency proofs for our method in both continuum and discrete finite domains for objective functions that are sums. In numerical experiments comparing against previous state-of-the-art methods, including those that also leverage sum or integral structure, our method performs as well or better across a wide range of problems and offers significant improvements when evaluations are noisy or the integrand varies smoothly in the integrated variables.

A group of transition probability functions form a Shannon's channel whereas a group of truth functions form a semantic channel. By the third kind of Bayes' theorem, we can directly convert a Shannon's channel into an optimized semantic channel. When a sample is not big enough, we can use a truth function with parameters to produce the likelihood function, then train the truth function by the conditional sampling distribution. The third kind of Bayes' theorem is proved. A semantic information theory is simply introduced. The semantic information measure reflects Popper's hypothesis-testing thought. The Semantic Information Method (SIM) adheres to maximum semantic information criterion which is compatible with maximum likelihood criterion and Regularized Least Squares criterion. It supports Wittgenstein's view: the meaning of a word lies in its use. Letting the two channels mutually match, we obtain the Channels' Matching (CM) algorithm for machine learning. The CM algorithm is used to explain the evolution of the semantic meaning of natural language, such as "Old age". The semantic channel for medical tests and the confirmation measures of test-positive and test-negative are discussed. The applications of the CM algorithm to semi-supervised learning and non-supervised learning are simply introduced. As a predictive model, the semantic channel fits variable sources and hence can overcome class-imbalance problem. The SIM strictly distinguishes statistical probability and logical probability and uses both at the same time. This method is compatible with the thoughts of Bayes, Fisher, Shannon, Zadeh, Tarski, Davidson, Wittgenstein, and Popper.It is a competitive alternative to Bayesian inference.

As more aspects of social interaction are digitally recorded, there is a growing need to develop privacy-preserving data analysis methods. Social scientists will be more likely to adopt these methods if doing so entails minimal change to their current methodology. Toward that end, we present a general and modular method for privatizing Bayesian inference for Poisson factorization, a broad class of models that contains some of the most widely used models in the social sciences. Our method satisfies local differential privacy, which ensures that no single centralized server need ever store the non-privatized data. To formulate our local-privacy guarantees, we introduce and focus on limited-precision local privacy---the local privacy analog of limited-precision differential privacy (Flood et al., 2013). We present two case studies, one involving social networks and one involving text corpora, that test our method's ability to form the posterior distribution over latent variables under different levels of noise, and demonstrate our method's utility over a na\"{i}ve approach, wherein inference proceeds as usual, treating the privatized data as if it were not privatized.

Speaker clustering is the task of differentiating speakers in a recording. In a way, the aim is to answer "who spoke when" in audio recordings. A common method used in industry is feature extraction directly from the recording thanks to MFCC features, and by using well-known techniques such as Gaussian Mixture Models (GMM) and Hidden Markov Models (HMM). In this paper, we studied neural networks (especially CNN) followed by clustering and audio processing in the quest to reach similar accuracy to state-of-the-art methods.

In this work we consider the problem of model selection in Gaussian Markov fields in the sample deficient scenario. The benchmark information-theoretic results in the case of d-regular graphs require the number of samples to be at least proportional to the logarithm of the number of vertices to allow consistent graph recovery. When the number of samples is less than this amount, reliable detection of all edges is impossible. In many applications, it is more important to learn the distribution of the edge (coupling) parameters over the network than the specific locations of the edges. Assuming that the entire graph can be partitioned into a number of spatial regions with similar edge parameters and reasonably regular boundaries, we develop new information-theoretic sample complexity bounds and show that even bounded number of samples can be enough to consistently recover these regions. We also introduce and analyze an efficient region growing algorithm capable of recovering the regions with high accuracy. We show that it is consistent and demonstrate its performance benefits in synthetic simulations. Markov random fields, or undirected probabilistic graphical models, provide a structured representation of the joint distributions of families of random variables. A Markov random field is an association of a set of random variables with the vertices of a graph, where the missing edges describe conditional independence properties among the variables [1]. It was shown by Hammersley and Clifford in their unpublished work [1] that the joint probability distribution specified by such a model factorizes according to the underlying graph. The practical importance of Markov random field is hard to overestimate. They have been applied to a large number of fields, including bioinformatics, social science, control theory, civil engineering, political science, epidemiology, image processing, marketing analysis, and many others. For instance, a graphical model may be used to represent friendships between people in a social network [3] or links between organisms with the propensity to spread an infectious disease [28]. This work was supported by the Fulbright Foundation and Office of Navy Research grant N00014-17-1-2075. 2 Given the graph structure, the most common computational tasks include calculating marginals, maximum a posteriori assignments, the partition function, sampling from the distribution and other questions of statistical inference. On the other hand, in many applications estimating the unknown edge structure of the underlying graph, also known as model selection or inverse problem, has attracted a great deal of attention. Naturally, both problems are essentially challenging especially in high dimensional scenarios and are known to be NPhard for general models [2, 3]. A variety of methods have been proposed to address this problem.

Being able to select the right model for inference is a crucial task. As our main example, we consider model selection for a normal linear model: Y Xβ, N (0,σ 2 I), (1) where Y is anN dimensional response vector,X is anN D dimensional design matrix and β is a D dimensional vector of regression parameters. Here the candidate models to be selected could refer to the sets of significant variables. In a Bayesian setting, we have a natural probabilistic evaluation of models 5 through posterior model probabilities. Depending on the objectives of the data analysis, we may be interested in assessing the belief on which is the "best" model or obtaining predictions with minimum error. Existing procedures to accomplish the aforementioned goals, however, will perform poorly under the presence of outliers and contaminations. In addition, 10 Markov chain Monte Carlo (MCMC) algorithms for these methods do not scale to big data situations. The goal of this paper is to investigate a "divide-and- conquer" method that integrates with existing Bayesian model selection techniques, in a way that is robust to outliers and, moreover, allows us to perform Bayesian model selection in parallel.