Prediction of events such as part replacement and failure events plays a critical role in reliability engineering. Event stream data are commonly observed in manufacturing and teleservice systems. Designing predictive models for individual units based on such event streams is challenging and an under-explored problem. In this work, we propose a non-parametric prognostic framework for individualized event prediction based on the inhomogeneous Poisson processes with a multivariate Gaussian convolution process (MGCP) prior on the intensity functions. The MGCP prior on the intensity functions of the inhomogeneous Poisson processes maps data from similar historical units to the current unit under study which facilitates sharing of information and allows for analysis of flexible event patterns. To facilitate inference, we derive a variational inference scheme for learning and estimation of parameters in the resulting MGCP modulated Poisson process model. Experimental results are shown on both synthetic data as well as real-world data for fleet based event prediction.

We consider a class of filtering problems for large populations where each individual is modeled by the same hidden Markov model (HMM). In this paper, we focus on aggregate inference problems in HMMs with discrete state space and continuous observation space. The continuous observations are aggregated in a way such that the individuals are indistinguishable from measurements. We propose an aggregate inference algorithm called continuous observation collective forward-backward algorithm. It extends the recently proposed collective forward-backward algorithm for aggregate inference in HMMs with discrete observations to the case of continuous observations. The efficacy of this algorithm is illustrated through several numerical experiments.

Calibrated estimates of uncertainty are critical for many real-world computer vision applications of deep learning. While there are several widely-used uncertainty estimation methods, dropout inference stands out for its simplicity and efficacy. This technique, however, requires multiple forward passes through the network during inference and therefore can be too resource-intensive to be deployed in real-time applications. We propose a simple, easy-to-optimize distillation method for learning the conditional predictive distribution of a pre-trained dropout model for fast, sample-free uncertainty estimation in computer vision tasks. We empirically test the effectiveness of the proposed method on both semantic segmentation and depth estimation tasks and demonstrate our method can significantly reduce the inference time, enabling real-time uncertainty quantification, while achieving improved quality of both the uncertainty estimates and predictive performance over the regular dropout model.

We develop a Bregman proximal gradient method for structure learning on linear structural causal models. While the problem is non-convex, has high curvature and is in fact NP-hard, Bregman gradient methods allow us to neutralize at least part of the impact of curvature by measuring smoothness against a highly nonlinear kernel. This allows the method to make longer steps and significantly improves convergence. Each iteration requires solving a Bregman proximal step which is convex and efficiently solvable for our particular choice of kernel. We test our method on various synthetic and real data sets.

In this paper we provide a new efficient algorithm for approximately computing the profile maximum likelihood (PML) distribution, a prominent quantity in symmetric property estimation. We provide an algorithm which matches the previous best known efficient algorithms for computing approximate PML distributions and improves when the number of distinct observed frequencies in the given instance is small. We achieve this result by exploiting new sparsity structure in approximate PML distributions and providing a new matrix rounding algorithm, of independent interest. Leveraging this result, we obtain the first provable computationally efficient implementation of PseudoPML, a general framework for estimating a broad class of symmetric properties. Additionally, we obtain efficient PML-based estimators for distributions with small profile entropy, a natural instance-based complexity measure. Further, we provide a simpler and more practical PseudoPML implementation that matches the best-known theoretical guarantees of such an estimator and evaluate this method empirically.

While deep neural networks provide good performance for a range of challenging tasks, calibration and uncertainty estimation remain major challenges. In this paper, we propose the amortized conditional normalized maximum likelihood (ACNML) method as a scalable general-purpose approach for uncertainty estimation, calibration, and out-of-distribution robustness with deep networks. Our algorithm builds on the conditional normalized maximum likelihood (CNML) coding scheme, which has minimax optimal properties according to the minimum description length principle, but is computationally intractable to evaluate exactly for all but the simplest of model classes. We propose to use approximate Bayesian inference technqiues to produce a tractable approximation to the CNML distribution. Our approach can be combined with any approximate inference algorithm that provides tractable posterior densities over model parameters. We demonstrate that ACNML compares favorably to a number of prior techniques for uncertainty estimation in terms of calibration on out-of-distribution inputs.

Loss functions are a cornerstone of machine learning and the starting point of most algorithms. Statistics and Bayesian decision theory have contributed, via properness, to elicit over the past decades a wide set of admissible losses in supervised learning, to which most popular choices belong (logistic, square, Matsushita, etc.). Rather than making a potentially biased ad hoc choice of the loss, there has recently been a boost in efforts to fit the loss to the domain at hand while training the model itself. The key approaches fit a canonical link, a function which monotonically relates the closed unit interval to R and can provide a proper loss via integration. In this paper, we rely on a broader view of proper composite losses and a recent construct from information geometry, source functions, whose fitting alleviates constraints faced by canonical links. We introduce a trick on squared Gaussian Processes to obtain a random process whose paths are compliant source functions with many desirable properties in the context of link estimation. Experimental results demonstrate substantial improvements over the state of the art.

The study of biological processes can greatly benefit from tools that automatically predict gene functions or directly cluster genes based on shared functionality. Existing data mining methods predict protein functionality by exploiting data obtained from high-throughput experiments or meta-scale information from public databases. Most existing prediction tools are targeted at predicting protein functions that are described in the gene ontology (GO). However, in many cases biologists wish to discover functionally related genes for which GO terms are inadequate. In this paper, we introduce a rich set of features and use them in conjunction with semisupervised learning approaches in order to expand an initial set of seed genes to a larger cluster of functionally related genes. Among all the semi-supervised methods that were evaluated, the framework of learning with positive and unlabeled examples (LPU) is shown to be especially appropriate for mining functionally related genes. When evaluated on experimentally validated benchmark data, the LPU approaches1 significantly outperform a standard supervised learning algorithm as well as an established state-of-the-art method. Given an initial set of seed genes, our best performing approach could be used to mine functionally related genes in a wide range of organisms.

Many important robotics problems are partially observable in the sense that a single visual or force-feedback measurement is insufficient to reconstruct the state. Standard approaches involve learning a policy over beliefs or observation-action histories. However, both of these have drawbacks; it is expensive to track the belief online, and it is hard to learn policies directly over histories. We propose a method for policy learning under partial observability called the Belief-Grounded Network (BGN) in which an auxiliary belief-reconstruction loss incentivizes a neural network to concisely summarize its input history. Since the resulting policy is a function of the history rather than the belief, it can be executed easily at runtime. We compare BGN against several baselines on classic benchmark tasks as well as three novel robotic touch-sensing tasks. BGN outperforms all other tested methods and its learned policies work well when transferred onto a physical robot.

Classical statistics is said to follow the frequentist approach because it interprets probability as the relative frequency of an event over the long run that is, after observing many trials. In the context of probabilities, an event is a combination of one or more elementary outcomes of an experiment, such as any of six equal results in rolls of two dice or an asset price dropping by 10 percent or more on a given day.