We present the very first robust Bayesian Online Changepoint Detection algorithm through General Bayesian Inference (GBI) with $\beta$-divergences. The resulting inference procedure is doubly robust for both the predictive and the changepoint (CP) posterior, with linear time and constant space complexity. We provide a construction for exponential models and demonstrate it on the Bayesian Linear Regression model. In so doing, we make two additional contributions: Firstly, we make GBI scalable using Structural Variational approximations that are exact as $\beta \to 0$. Secondly, we give a principled way of choosing the divergence parameter $\beta$ by minimizing expected predictive loss on-line. Reducing False Discovery Rates of \CPs from up to 99\% to 0\% on real world data, this offers the state of the art.

Access to a large variety of data across a massive population has made it possible to predict customer purchase patterns and responses to marketing campaigns. In particular, accurate demand forecasts for popular products with frequent repeat purchases are essential since these products are one of the main drivers of profits. However, buyer purchase patterns are extremely diverse and sparse on a per-product level due to population heterogeneity as well as dependence in purchase patterns across product categories. Traditional methods in survival analysis have proven effective in dealing with censored data by assuming parametric distributions on inter-arrival times. Distributional parameters are then fitted, typically in a regression framework. On the other hand, neural-network based models take a non-parametric approach to learn relations from a larger functional class. However, the lack of distributional assumptions make it difficult to model partially observed data. In this paper, we model directly the inter-arrival times as well as the partially observed information at each time step in a survival-based approach using Recurrent Neural Networks (RNN) to model purchase times jointly over several products. Instead of predicting a point estimate for inter-arrival times, the RNN outputs parameters that define a distributional estimate. The loss function is the negative log-likelihood of these parameters given partially observed data. This approach allows one to leverage both fully observed data as well as partial information. By externalizing the censoring problem through a log-likelihood loss function, we show that substantial improvements over state-of-the-art machine learning methods can be achieved. We present experimental results based on two open datasets as well as a study on a real dataset from a large retailer.

Many data generating processes involve latent random variables over discrete combinatorial spaces whose size grows factorially with the dataset. In these settings, existing posterior inference methods can be inaccurate and/or very slow. In this work we develop methods for efficient amortized approximate Bayesian inference over discrete combinatorial spaces, with applications to random permutations, probabilistic clustering (such as Dirichlet process mixture models) and random communities (such as stochastic block models). The approach is based on mapping distributed, symmetry-invariant representations of discrete arrangements into conditional probabilities. The resulting algorithms parallelize easily, yield iid samples from the approximate posteriors, and can easily be applied to both conjugate and non-conjugate models, as training only requires samples from the generative model.

Deep learning provides a powerful tool for machine perception when the observations resemble the training data. However, real-world robotic systems must react intelligently to their observations even in unexpected circumstances. This requires a system to reason about its own uncertainty given unfamiliar, out-of-distribution observations. Approximate Bayesian approaches are commonly used to estimate uncertainty for neural network predictions, but can struggle with out-of-distribution observations. Generative models can in principle detect out-of-distribution observations as those with a low estimated density. However, the mere presence of an out-of-distribution input does not by itself indicate an unsafe situation. In this paper, we present a method for uncertainty-aware robotic perception that combines generative modeling and model uncertainty to cope with uncertainty stemming from out-of-distribution states. Our method estimates an uncertainty measure about the model's prediction, taking into account an explicit (generative) model of the observation distribution to handle out-of-distribution inputs. This is accomplished by probabilistically projecting observations onto the training distribution, such that out-of-distribution inputs map to uncertain in-distribution observations, which in turn produce uncertain task-related predictions, but only if task-relevant parts of the image change. We evaluate our method on an action-conditioned collision prediction task with both simulated and real data, and demonstrate that our method of projecting out-of-distribution observations improves the performance of four standard Bayesian and non-Bayesian neural network approaches, offering more favorable trade-offs between the proportion of time a robot can remain autonomous and the proportion of impending crashes successfully avoided.

In this paper we propose a method to model speaker and session variability and able to generate likelihood ratios using neural networks in an end-to-end phrase dependent speaker verification system. As in Joint Factor Analysis, the model uses tied hidden variables to model speaker and session variability and a MAP adaptation of some of the parameters of the model. In the training procedure our method jointly estimates the network parameters and the values of the speaker and channel hidden variables. This is done in a two-step backpropagation algorithm, first the network weights and factor loading matrices are updated and then the hidden variables, whose gradients are calculated by aggregating the corresponding speaker or session frames, since these hidden variables are tied. The last layer of the network is defined as a linear regression probabilistic model whose inputs are the previous layer outputs. This choice has the advantage that it produces likelihoods and additionally it can be adapted during the enrolment using MAP without the need of a gradient optimization. The decisions are made based on the ratio of the output likelihoods of two neural network models, speaker adapted and universal background model. The method was evaluated on the RSR2015 database.

There are great interests as well as many challenges in applying reinforcement learning (RL) to recommendation systems. In this setting, an online user is the environment; neither the reward function nor the environment dynamics are clearly defined, making the application of RL challenging. In this paper, we propose a novel model-based reinforcement learning framework for recommendation systems, where we develop a generative adversarial network to imitate user behavior dynamics and learn her reward function. Using this user model as the simulation environment, we develop a novel DQN algorithm to obtain a combinatorial recommendation policy which can handle a large number of candidate items efficiently. In our experiments with real data, we show this generative adversarial user model can better explain user behavior than alternatives, and the RL policy based on this model can lead to a better long-term reward for the user and higher click rate for the system.

The rising volume of datasets has made training machine learning (ML) models a major computational cost in the enterprise. Given the iterative nature of model and parameter tuning, many analysts use a small sample of their entire data during their initial stage of analysis to make quick decisions (e.g., what features or hyperparameters to use) and use the entire dataset only in later stages (i.e., when they have converged to a specific model). This sampling, however, is performed in an ad-hoc fashion. Most practitioners cannot precisely capture the effect of sampling on the quality of their model, and eventually on their decision-making process during the tuning phase. Moreover, without systematic support for sampling operators, many optimizations and reuse opportunities are lost. In this paper, we introduce BlinkML, a system for fast, quality-guaranteed ML training. BlinkML allows users to make error-computation tradeoffs: instead of training a model on their full data (i.e., full model), BlinkML can quickly train an approximate model with quality guarantees using a sample. The quality guarantees ensure that, with high probability, the approximate model makes the same predictions as the full model. BlinkML currently supports any ML model that relies on maximum likelihood estimation (MLE), which includes Generalized Linear Models (e.g., linear regression, logistic regression, max entropy classifier, Poisson regression) as well as PPCA (Probabilistic Principal Component Analysis). Our experiments show that BlinkML can speed up the training of large-scale ML tasks by 6.26x-629x while guaranteeing the same predictions, with 95% probability, as the full model.

A common challenge in estimating parameters of probability density functions is the intractability of the normalizing constant. While in such cases maximum likelihood estimation may be implemented using numerical integration, the approach becomes computationally intensive. The score matching method of Hyv\"arinen [2005] avoids direct calculation of the normalizing constant and yields closed-form estimates for exponential families of continuous distributions over $\mathbb{R}^m$. Hyv\"arinen [2007] extended the approach to distributions supported on the non-negative orthant, $\mathbb{R}_+^m$. In this paper, we give a generalized form of score matching for non-negative data that improves estimation efficiency. As an example, we consider a general class of pairwise interaction models. Addressing an overlooked inexistence problem, we generalize the regularized score matching method of Lin et al. [2016] and improve its theoretical guarantees for non-negative Gaussian graphical models.

We address the problem of two-variable causal inference. This task is to infer an existing causal relation between two random variables, i.e. $X \rightarrow Y$ or $Y \rightarrow X$, from purely observational data. We briefly review a number of state-of-the-art methods for this, including very recent ones. A novel inference method is introduced, Bayesian Causal Inference (BCI), which assumes a generative Bayesian hierarchical model to pursue the strategy of Bayesian model selection. In the model the distribution of the cause variable is given by a Poisson lognormal distribution, which allows to explicitly regard discretization effects. We assume Fourier diagonal Field covariance operators. The generative model assumed provides synthetic causal data for benchmarking our model in comparison to existing State-of-the-art models, namely LiNGAM, ANM-HSIC, ANM-MML, IGCI and CGNN. We explore how well the above methods perform in case of high noise settings, strongly discretized data and very sparse data. BCI performs generally reliable with synthetic data as well as with the real world TCEP benchmark set, with an accuracy comparable to state-of-the-art algorithms.

The Normal Means problem plays a fundamental role in many areas of modern high-dimensional statistics, both in theory and practice. And the Empirical Bayes (EB) approach to solving this problem has been shown to be highly effective, again both in theory and practice. However, almost all EB treatments of the Normal Means problem assume that the observations are independent. In practice correlations are ubiquitous in real-world applications, and these correlations can grossly distort EB estimates. Here, exploiting theory from Schwartzman (2010), we develop new EB methods for solving the Normal Means problem that take account of unknown correlations among observations. We provide practical software implementations of these methods, and illustrate them in the context of large-scale multiple testing problems and False Discovery Rate (FDR) control. In realistic numerical experiments our methods compare favorably with other commonly-used multiple testing methods.