Is probabilistic programming and Bayesian reasoning algorithms the next big thing in machine learning? The idea behind the probabilistic programming to machine learning is that the model of the data can be separated from the algorithms that do inference on the model. The allows you to devote your energy to building models tailored to your decision problem, as opposed to constraining your problem so it works with some machine learning tool. This idea opens machine learning to domain experts. Indeed, probabilistic programming grew out of probabilistic graphical models, which revolutionized AI by enabling expert knowledge to be built into graphs powered by Bayesian inference.

We introduce a novel approach for estimating Latent Dirichlet Allocation (LDA) parameters from collapsed Gibbs samples (CGS), by leveraging the full conditional distributions over the latent variable assignments to efficiently average over multiple samples, for little more computational cost than drawing a single additional collapsed Gibbs sample. Our approach can be understood as adapting the soft clustering methodology of Collapsed Variational Bayes (CVB0) to CGS parameter estimation, in order to get the best of both techniques. Our estimators can straightforwardly be applied to the output of any existing implementation of CGS, including modern accelerated variants. We perform extensive empirical comparisons of our estimators with those of standard collapsed inference algorithms on real-world data for both unsupervised LDA and Prior-LDA, a supervised variant of LDA for multi-label classification. Our results show a consistent advantage of our approach over traditional CGS under all experimental conditions, and over CVB0 inference in the majority of conditions. More broadly, our results highlight the importance of averaging over multiple samples in LDA parameter estimation, and the use of efficient computational techniques to do so.

This book provides an introduction to statistical learning methods. It is aimed for upper level undergraduate students, masters students and Ph.D. students in the non-mathematical sciences. The book also contains a number of R labs with detailed explanations on how to implement the various methods in real life settings, and should be a valuable resource for a practicing data scientist.

Social networks are getting closer to our real physical world. People share the exact location and time of their check-ins and are influenced by their friends. Modeling the spatio-temporal behavior of users in social networks is of great importance for predicting the future behavior of users, controlling the users' movements, and finding the latent influence network. It is observed that users have periodic patterns in their movements. Also, they are influenced by the locations that their close friends recently visited. Leveraging these two observations, we propose a probabilistic model based on a doubly stochastic point process with a periodic decaying kernel for the time of check-ins and a time-varying multinomial distribution for the location of check-ins of users in the location-based social networks. We learn the model parameters using an efficient EM algorithm, which distributes over the users. Experiments on synthetic and real data gathered from Foursquare show that the proposed inference algorithm learns the parameters efficiently and our model outperforms the other alternatives in the prediction of time and location of check-ins.

We study the problem of cooperative inference where a group of agents interact over a network and seek to estimate a joint parameter that best explains a set of observations. Agents do not know the network topology or the observations of other agents. We explore a variational interpretation of the Bayesian posterior density, and its relation to the stochastic mirror descent algorithm, to propose a new distributed learning algorithm. We show that, under appropriate assumptions, the beliefs generated by the proposed algorithm concentrate around the true parameter exponentially fast. We provide explicit non-asymptotic bounds for the convergence rate. Moreover, we develop explicit and computationally efficient algorithms for observation models belonging to exponential families.

Many machine learning applications are based on data collected from people, such as their tastes and behaviour as well as biological traits and genetic data. Regardless of how important the application might be, one has to make sure individuals' identities or the privacy of the data are not compromised in the analysis. Differential privacy constitutes a powerful framework that prevents breaching of data subject privacy from the output of a computation. Differentially private versions of many important Bayesian inference methods have been proposed, but there is a lack of an efficient unified approach applicable to arbitrary models. In this contribution, we propose a differentially private variational inference method with a very wide applicability. It is built on top of doubly stochastic variational inference, a recent advance which provides a variational solution to a large class of models. We add differential privacy into doubly stochastic variational inference by clipping and perturbing the gradients. The algorithm is made more efficient through privacy amplification from subsampling. We demonstrate the method can reach an accuracy close to non-private level under reasonably strong privacy guarantees, clearly improving over previous sampling-based alternatives especially in the strong privacy regime.

I have made some progress with my work on combining independent evidence using a Bayesian approach but eschewing standard Bayesian updating. I found a neat analytical way of doing this, to a very good approximation, in cases where each estimate of a parameter corresponds to the ratio of two variables each determined with normal error, the fractional uncertainty in the numerator and denominator variables differing between the types of evidence. This seems a not uncommon situation in science, and it is a good approximation to that which exists when estimating climate sensitivity. I have had a manuscript in which I develop and test this method accepted by the Journal of Statistical Planning and Inference (for a special issue on Confidence Distributions edited by Tore Schweder and Nils Hjort). Frequentist coverage is almost exact using my analytical solution, based on combining Jeffreys' priors in quadrature, whereas Bayesian updating produces far poorer probability matching.

Graphical causal models are an important tool for knowledge discovery because they can represent both the causal relations between variables and the multivariate probability distributions over the data. Once learned, causal graphs can be used for classification, feature selection and hypothesis generation, while revealing the underlying causal network structure and thus allowing for arbitrary likelihood queries over the data. However, current algorithms for learning sparse directed graphs are generally designed to handle only one type of data (continuous-only or discrete-only), which limits their applicability to a large class of multi-modal biological datasets that include mixed type variables. To address this issue, we developed new methods that modify and combine existing methods for finding undirected graphs with methods for finding directed graphs. These hybrid methods are not only faster, but also perform better than the directed graph estimation methods alone for a variety of parameter settings and data set sizes. Here, we describe a new conditional independence test for learning directed graphs over mixed data types and we compare performances of different graph learning strategies on synthetic data.

In the previous post, we discussed the motivation behind Maximum Likelihood Estimate and how to calculate it. We also learned a few tricks about calculating the log likelihood of a function by citing the application of monotonic functions, and how they make the entire process of estimating the critical points of a function much easier as they preserve those critical points. Put the #tails (0) and #heads (2) in the equation of theta_MLE, This result tells us that the probability of next flip being Tails is 0 (i.e., it predicts that no flip is ever gonna turn up Tails the coin is always going to show Heads), and it is glaringly obvious that this is not the case (barring the extreme case where the coin is heavily loaded). Now, this poses a big problem in the Parameter Estimation process because it does not give us the accurate probability of the next flip. We know that even a fair coin has a 25% chance of showing two Heads in a row (0.5 x 0.5 0.25).

In this paper we study the problem of noisy tensor completion for tensors that admit a canonical polyadic or CANDECOMP/PARAFAC (CP) decomposition with one of the factors being sparse. We present general theoretical error bounds for an estimate obtained by using a complexity-regularized maximum likelihood principle and then instantiate these bounds for the case of additive white Gaussian noise. We also provide an ADMM-type algorithm for solving the complexity-regularized maximum likelihood problem and validate the theoretical finding via experiments on synthetic data set.