Network growth processes can be understood as generative models of the structure and history of complex networks. This point of view naturally leads to the problem of network archaeology: Reconstructing all the past states of a network from its structure---a difficult permutation inference problem. In this paper, we introduce a Bayesian formulation of network archaeology, with a generalization of preferential attachment as our generative mechanism. We develop a sequential importance sampling algorithm to evaluate the posterior averages of this model, as well as an efficient heuristic that uncovers the history of a network in linear time. We use these methods to identify and characterize a phase transition in the quality of the reconstructed history, when they are applied to artificial networks generated by the model itself. Despite the existence of a no-recovery phase, we find that non-trivial inference is possible in a large portion of the parameter space as well as on empirical data.

The randomized experiment is an important tool for inferring the causal impact of an intervention. The recent literature on statistical learning methods for heterogeneous treatment effects demonstrates the utility of estimating the marginal conditional average treatment effect (MCATE), i.e., the average treatment effect for a subpopulation of respondents who share a particular subset of covariates. However, each proposed method makes its own set of restrictive assumptions about the intervention's effects, the underlying data generating processes, and which subpopulations (MCATEs) to explicitly estimate. Moreover, the majority of the literature provides no mechanism to identify which subpopulations are the most affected--beyond manual inspection--and provides little guarantee on the correctness of the identified subpopulations. Therefore, we propose Treatment Effect Subset Scan (TESS), a new method for discovering which subpopulation in a randomized experiment is most significantly affected by a treatment. We frame this challenge as a pattern detection problem where we maximize a nonparametric scan statistic (measurement of distributional divergence) over subpopulations, while being parsimonious in which specific subpopulations to evaluate. Furthermore, we identify the subpopulation which experiences the largest distributional change as a result of the intervention, while making minimal assumptions about the intervention's effects or the underlying data generating process. In addition to the algorithm, we demonstrate that the asymptotic Type I and II error can be controlled, and provide sufficient conditions for detection consistency---i.e., exact identification of the affected subpopulation. Finally, we validate the efficacy of the method by discovering heterogeneous treatment effects in simulations and in real-world data from a well-known program evaluation study.

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 )

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.

Measuring uncertainty is a promising technique for detecting adversarial examples, crafted inputs on which the model predicts an incorrect class with high confidence. But many measures of uncertainty exist, including predictive en- tropy and mutual information, each capturing different types of uncertainty. We study these measures, and shed light on why mutual information seems to be effective at the task of adversarial example detection. We highlight failure modes for MC dropout, a widely used approach for estimating uncertainty in deep models. This leads to an improved understanding of the drawbacks of current methods, and a proposal to improve the quality of uncertainty estimates using probabilistic model ensembles. We give illustrative experiments using MNIST to demonstrate the intuition underlying the different measures of uncertainty, as well as experiments on a real world Kaggle dogs vs cats classification dataset.

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.

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.

While off-policy temporal difference methods have been broadly used in reinforcement learning due to their efficiency and simple implementation, their Bayesian counterparts have been relatively understudied. This is mainly because the max operator in the Bellman optimality equation brings non-linearity and inconsistent distributions over value function. In this paper, we introduce a new Bayesian approach to off-policy TD methods using Assumed Density Filtering, called ADFQ, which updates beliefs on action-values (Q) through an online Bayesian inference method. Uncertainty measures in the beliefs not only are used in exploration but they provide a natural regularization in the belief updates. We also present a connection between ADFQ and Q-learning. Our empirical results show the proposed ADFQ algorithms outperform comparing algorithms in several task domains. Moreover, our algorithms improve general drawbacks in BRL such as efficiency, usage of uncertainty, and nonlinearity.