Based on non-local prior distributions, we propose a Bayesian model selection (BMS) procedure for boundary detection in a sequence of data with multiple systematic mean changes. The BMS method can effectively suppress the non-boundary spike points with large instantaneous changes. We speed up the algorithm by reducing the multiple change points to a series of single change point detection problems. We establish the consistency of the estimated number and locations of the change points under various prior distributions. Extensive simulation studies are conducted to compare the BMS with existing methods, and our approach is illustrated with application to the magnetic resonance imaging guided radiation therapy data.

Computable Stein discrepancies have been deployed for a variety of applications, ranging from sampler selection in posterior inference to approximate Bayesian inference to goodness-of-fit testing. Existing convergence-determining Stein discrepancies admit strong theoretical guarantees but suffer from a computational cost that grows quadratically in the sample size. While linear-time Stein discrepancies have been proposed for goodness-of-fit testing, they exhibit avoidable degradations in testing power—even when power is explicitly optimized. To address these shortcomings, we introduce feature Stein discrepancies (ΦSDs), a new family of quality measures that can be cheaply approximated using importance sampling. We show how to construct ΦSDs that provably determine the convergence of a sample to its target and develop high-accuracy approximations—random ΦSDs (RΦSDs)—which are computable in near-linear time. In our experiments with sampler selection for approximate posterior inference and goodness-of-fit testing, RΦSDs perform as well or better than quadratic-time KSDs while being orders of magnitude faster to compute.

Probability estimation is one of the fundamental tasks in statistics and machine learning. However, standard methods for probability estimation on discrete objects do not handle object structure in a satisfactory manner. In this paper, we derive a general Bayesian network formulation for probability estimation on leaf-labeled trees that enables flexible approximations which can generalize beyond observations. We show that efficient algorithms for learning Bayesian networks can be easily extended to probability estimation on this challenging structured space. Experiments on both synthetic and real data show that our methods greatly outperform the current practice of using the empirical distribution, as well as a previous effort for probability estimation on trees.

Fine-Grained Visual Classification (FGVC) is an important computer vision problem that involves small diversity within the different classes, and often requires expert annotators to collect data. Utilizing this notion of small visual diversity, we revisit Maximum-Entropy learning in the context of fine-grained classification, and provide a training routine that maximizes the entropy of the output probability distribution for training convolutional neural networks on FGVC tasks. We provide a theoretical as well as empirical justification of our approach, and achieve state-of-the-art performance across a variety of classification tasks in FGVC, that can potentially be extended to any fine-tuning task. Our method is robust to different hyperparameter values, amount of training data and amount of training label noise and can hence be a valuable tool in many similar problems.

By providing a simple and efficient way of computing low-variance gradients of continuous random variables, the reparameterization trick has become the technique of choice for training a variety of latent variable models. However, it is not applicable to a number of important continuous distributions. We introduce an alternative approach to computing reparameterization gradients based on implicit differentiation and demonstrate its broader applicability by applying it to Gamma, Beta, Dirichlet, and von Mises distributions, which cannot be used with the classic reparameterization trick. Our experiments show that the proposed approach is faster and more accurate than the existing gradient estimators for these distributions.

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.

The International Classification of Functioning, Disability, and Health for Children and Youth (ICF-CY) is a scaffold for designating and systematizing data on functioning and disability. It offers a standard semantic and a theoretical foundation for the demarcation and extent of wellbeing and infirmity. The multidimensional layout of ICF-CY comprehends a plethora of information with about 1400 categories making it difficult to analyze. Our research proposes a predictive model that classify self-care problems on Self-Care Activities Dataset based on the ICF- CY. The data used in this study resides 206 attributes of 70 children with motor and physical disability. Our study implements, compare and analyze Random Forest, Support vector machine, Naive Bayes, Hoeffding tree, and Lazy locally weighted learning using two-tailed T-test at 95% confidence interval. Boruta algorithm involved in the study minimizes the data dimensionality to advocate the minimal-optimal set of predictors. Random forest gave the best classification accuracy of 84.75%; root mean squared error of 0.18 and receiver operating characteristic of 0.99. Predictive analytics can simplify the usage of ICF-CY by automating the classification process of disability, functioning, and health.

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.