We consider the estimation of Dirichlet Process Mixture Models (DPMMs) in distributed environments, where data are distributed across multiple computing nodes. A key advantage of Bayesian nonparametric models such as DPMMs is that they allow new components to be introduced on the fly as needed. This, however, posts an important challenge to distributed estimation -- how to handle new components efficiently and consistently. To tackle this problem, we propose a new estimation method, which allows new components to be created locally in individual computing nodes. Components corresponding to the same cluster will be identified and merged via a probabilistic consolidation scheme. In this way, we can maintain the consistency of estimation with very low communication cost. Experiments on large real-world data sets show that the proposed method can achieve high scalability in distributed and asynchronous environments without compromising the mixing performance.

We revisit the problem of estimating the parameters of a partially observed diffusion process, consisting of a hidden state process and an observed process, with a continuous time parameter. The estimation is to be done online, i.e. the parameter estimate should be updated recursively based on the observation filtration. Here, we use an old but under-exploited representation of the incomplete-data log-likelihood function in terms of the filter of the hidden state from the observations. By performing a stochastic gradient ascent, we obtain a fully recursive algorithm for the time evolution of the parameter estimate. We prove the convergence of the algorithm under suitable conditions regarding the ergodicity of the process consisting of state, filter, and tangent filter. Additionally, our parameter estimation is shown numerically to have the potential of improving suboptimal filters, and can be applied even when the system is not identifiable due to parameter redundancies. Online parameter estimation is a challenging problem that is ubiquitous in fields such as robotics, neuroscience, or finance in order to design adaptive filters and optimal controllers for unknown or changing systems.

Some of the most common examples of machine learning are Netflix's algorithms to make movie suggestions based on movies you have watched in the past or Amazon's algorithms that recommend books based on books you have bought before. The textbook that we used is one of the AI classics: Peter Norvig's Artificial Intelligence -- A Modern Approach, in which we covered major topics including intelligent agents, problem-solving by searching, adversarial search, probability theory, multi-agent systems, social AI, philosophy/ethics/future of AI. Machine learning algorithms can be divided into 3 broad categories -- supervised learning, unsupervised learning, and reinforcement learning.Supervised learning is useful in cases where a property (label) is available for a certain dataset (training set), but is missing and needs to be predicted for other instances. You can think of linear regression as the task of fitting a straight line through a set of points.

We consider the problem of non-parametric Conditional Independence testing (CI testing) for continuous random variables. Given i.i.d samples from the joint distribution $f(x,y,z)$ of continuous random vectors $X,Y$ and $Z,$ we determine whether $X \perp Y | Z$. We approach this by converting the conditional independence test into a classification problem. This allows us to harness very powerful classifiers like gradient-boosted trees and deep neural networks. These models can handle complex probability distributions and allow us to perform significantly better compared to the prior state of the art, for high-dimensional CI testing. The main technical challenge in the classification problem is the need for samples from the conditional product distribution $f^{CI}(x,y,z) = f(x|z)f(y|z)f(z)$ -- the joint distribution if and only if $X \perp Y | Z.$ -- when given access only to i.i.d. samples from the true joint distribution $f(x,y,z)$. To tackle this problem we propose a novel nearest neighbor bootstrap procedure and theoretically show that our generated samples are indeed close to $f^{CI}$ in terms of total variational distance. We then develop theoretical results regarding the generalization bounds for classification for our problem, which translate into error bounds for CI testing. We provide a novel analysis of Rademacher type classification bounds in the presence of non-i.i.d near-independent samples. We empirically validate the performance of our algorithm on simulated and real datasets and show performance gains over previous methods.

In this paper we introduce ZhuSuan, a python probabilistic programming library for Bayesian deep learning, which conjoins the complimentary advantages of Bayesian methods and deep learning. ZhuSuan is built upon Tensorflow. Unlike existing deep learning libraries, which are mainly designed for deterministic neural networks and supervised tasks, ZhuSuan is featured for its deep root into Bayesian inference, thus supporting various kinds of probabilistic models, including both the traditional hierarchical Bayesian models and recent deep generative models. We use running examples to illustrate the probabilistic programming on ZhuSuan, including Bayesian logistic regression, variational auto-encoders, deep sigmoid belief networks and Bayesian recurrent neural networks.

Semi-supervised and unsupervised systems provide operators with invaluable support and can tremendously reduce the operators load. In the light of the necessity to process large volumes of video data and provide autonomous decisions, this work proposes new learning algorithms for activity analysis in video. The activities and behaviours are described by a dynamic topic model. Two novel learning algorithms based on the expectation maximisation approach and variational Bayes inference are proposed. Theoretical derivations of the posterior of model parameters are given. The designed learning algorithms are compared with the Gibbs sampling inference scheme introduced earlier in the literature. A detailed comparison of the learning algorithms is presented on real video data. We also propose an anomaly localisation procedure, elegantly embedded in the topic modeling framework. The proposed framework can be applied to a number of areas, including transportation systems, security and surveillance.

The Poisson model is frequently employed to describe count data, but in a Bayesian context it leads to an analytically intractable posterior probability distribution. In this work, we analyze a variational Gaussian approximation to the posterior distribution arising from the Poisson model with a Gaussian prior. This is achieved by seeking an optimal Gaussian distribution minimizing the Kullback-Leibler divergence from the posterior distribution to the approximation, or equivalently maximizing the lower bound for the model evidence. We derive an explicit expression for the lower bound, and show the existence and uniqueness of the optimal Gaussian approximation. The lower bound functional can be viewed as a variant of classical Tikhonov regularization that penalizes also the covariance. Then we develop an efficient alternating direction maximization algorithm for solving the optimization problem, and analyze its convergence. We discuss strategies for reducing the computational complexity via low rank structure of the forward operator and the sparsity of the covariance. Further, as an application of the lower bound, we discuss hierarchical Bayesian modeling for selecting the hyperparameter in the prior distribution, and propose a monotonically convergent algorithm for determining the hyperparameter. We present extensive numerical experiments to illustrate the Gaussian approximation and the algorithms.

Identifying context-specific entity networks from aggregated data is an important task, arising often in bioinformatics and neuroimaging. Computationally, this task can be formulated as jointly estimating multiple different, but related, sparse Undirected Graphical Models (UGM) from aggregated samples across several contexts. Previous joint-UGM studies have mostly focused on sparse Gaussian Graphical Models (sGGMs) and can't identify context-specific edge patterns directly. We, therefore, propose a novel approach, SIMULE (detecting Shared and Individual parts of MULtiple graphs Explicitly) to learn multi-UGM via a constrained L1 minimization. SIMULE automatically infers both specific edge patterns that are unique to each context and shared interactions preserved among all the contexts. Through the L1 constrained formulation, this problem is cast as multiple independent subtasks of linear programming that can be solved efficiently in parallel. In addition to Gaussian data, SIMULE can also handle multivariate Nonparanormal data that greatly relaxes the normality assumption that many real-world applications do not follow. We provide a novel theoretical proof showing that SIMULE achieves a consistent result at the rate O(log(Kp)/n_{tot}). On multiple synthetic datasets and two biomedical datasets, SIMULE shows significant improvement over state-of-the-art multi-sGGM and single-UGM baselines.

Principal component analysis (PCA) is very popular to perform dimension reduction. The selection of the number of significant components is essential but often based on some practical heuristics depending on the application. Only few works have proposed a probabilistic approach able to infer the number of significant components. To this purpose, this paper introduces a Bayesian nonparametric principal component analysis (BNP-PCA). The proposed model projects observations onto a random orthogonal basis which is assigned a prior distribution defined on the Stiefel manifold. The prior on factor scores involves an Indian buffet process to model the uncertainty related to the number of components. The parameters of interest as well as the nuisance parameters are finally inferred within a fully Bayesian framework via Monte Carlo sampling. A study of the (in-)consistence of the marginal maximum a posteriori estimator of the latent dimension is carried out. A new estimator of the subspace dimension is proposed. Moreover, for sake of statistical significance, a Kolmogorov-Smirnov test based on the posterior distribution of the principal components is used to refine this estimate. The behaviour of the algorithm is first studied on various synthetic examples. Finally, the proposed BNP dimension reduction approach is shown to be easily yet efficiently coupled with clustering or latent factor models within a unique framework.

We introduce an unsupervised discriminative model for the task of retrieving experts in online document collections. We exclusively employ textual evidence and avoid explicit feature engineering by learning distributed word representations in an unsupervised way. We compare our model to state-of-the-art unsupervised statistical vector space and probabilistic generative approaches. Our proposed log-linear model achieves the retrieval performance levels of state-of-the-art document-centric methods with the low inference cost of so-called profile-centric approaches. It yields a statistically significant improved ranking over vector space and generative models in most cases, matching the performance of supervised methods on various benchmarks. That is, by using solely text we can do as well as methods that work with external evidence and/or relevance feedback. A contrastive analysis of rankings produced by discriminative and generative approaches shows that they have complementary strengths due to the ability of the unsupervised discriminative model to perform semantic matching.