Product risk assessment is the overall process of determining whether a product, which could be anything from a type of washing machine to a type of teddy bear, is judged safe for consumers to use. There are several methods used for product risk assessment, including RAPEX, which is the primary method used by regulators in the UK and EU. However, despite its widespread use, we identify several limitations of RAPEX including a limited approach to handling uncertainty and the inability to incorporate causal explanations for using and interpreting test data. In contrast, Bayesian Networks (BNs) are a rigorous, normative method for modelling uncertainty and causality which are already used for risk assessment in domains such as medicine and finance, as well as critical systems generally. This article proposes a BN model that provides an improved systematic method for product risk assessment that resolves the identified limitations with RAPEX. We use our proposed method to demonstrate risk assessments for a teddy bear and a new uncertified kettle for which there is no testing data and the number of product instances is unknown. We show that, while we can replicate the results of the RAPEX method, the BN approach is more powerful and flexible.

Sparse sequences of neural spikes are posited to underlie aspects of working memory, motor production, and learning. Discovering these sequences in an unsupervised manner is a longstanding problem in statistical neuroscience. Promising recent work utilized a convolutive nonnegative matrix factorization model to tackle this challenge. However, this model requires spike times to be discretized, utilizes a sub-optimal least-squares criterion, and does not provide uncertainty estimates for model predictions or estimated parameters. We address each of these shortcomings by developing a point process model that characterizes fine-scale sequences at the level of individual spikes and represents sequence occurrences as a small number of marked events in continuous time. This ultra-sparse representation of sequence events opens new possibilities for spike train modeling. For example, we introduce learnable time warping parameters to model sequences of varying duration, which have been experimentally observed in neural circuits. We demonstrate these advantages on experimental recordings from songbird higher vocal center and rodent hippocampus.

As local explanations of black box models are increasingly being employed to establish model credibility in high stakes settings, it is important to ensure that these explanations are accurate and reliable. However, local explanations generated by existing techniques are often prone to high variance. Further, these techniques are computationally inefficient, require significant hyper-parameter tuning, and provide little insight into the quality of the resulting explanations. We identify lack of uncertainty modeling as a main cause of these challenges and develop a novel set of tools for analyzing explanation uncertainty in a Bayesian framework. In particular, we estimate credible intervals (CIs) that capture the uncertainty associated with each feature importance in local explanations. These credible intervals are tight when we have high confidence in the feature importances of a local explanation. The CIs are also informative both for estimating how many perturbations we need to sample -- sampling can proceed until the CIs are sufficiently narrow -- and where to sample -- sampling in regions with high predictive uncertainty leads to faster convergence. We instantiate this framework to generate Bayesian versions of LIME and KernelSHAP. Experimental evaluation with multiple real world datasets and user studies demonstrate the efficacy of our framework and the resulting explanations.

Quasi-Maximum Likelihood (QML) procedures are theoretically appealing and widely used for statistical inference. While there are extensive references on QML estimation in batch settings, the QML estimation in streaming settings has attracted little attention until recently. An investigation of the convergence properties of the QML procedure in a general conditionally heteroscedastic time series model is conducted, and the classical batch optimization routines extended to the framework of streaming and large-scale problems. An adaptive recursive estimation routine for GARCH models named AdaVol is presented. The AdaVol procedure relies on stochastic approximations combined with the technique of Variance Targeting Estimation (VTE). This recursive method has computationally efficient properties, while VTE alleviates some convergence difficulties encountered by the usual QML estimation due to a lack of convexity. Empirical results demonstrate a favorable trade-off between AdaVol's stability and the ability to adapt to time-varying estimates for real-life data.

In this paper, we investigate the problem of computing Bayesian estimators using Langevin Monte-Carlo type approximation. The novelty of this paper is to consider together the statistical and numerical counterparts (in a general log-concave setting). More precisely, we address the following question: given $n$ observations in $\mathbb{R}^q$ distributed under an unknown probability $\mathbb{P}_{\theta^\star}$ with $\theta^\star \in \mathbb{R}^d$ , what is the optimal numerical strategy and its cost for the approximation of $\theta^\star$ with the Bayesian posterior mean? To answer this question, we establish some quantitative statistical bounds related to the underlying Poincar\'e constant of the model and establish new results about the numerical approximation of Gibbs measures by Cesaro averages of Euler schemes of (over-damped) Langevin diffusions. These last results include in particular some quantitative controls in the weakly convex case based on new bounds on the solution of the related Poisson equation of the diffusion.

Modifying the reward-biased maximum likelihood method originally proposed in the adaptive control literature, we propose novel learning algorithms to handle the explore-exploit trade-off in linear bandits problems as well as generalized linear bandits problems. We develop novel index policies that we prove achieve order-optimality, and show that they achieve empirical performance competitive with the state-of-the-art benchmark methods in extensive experiments. The new policies achieve this with low computation time per pull for linear bandits, and thereby resulting in both favorable regret as well as computational efficiency.

The SIGTYP 2020 shared task (Bjerva et al., 2020) We reach the accuracy of 70.7% on the test data and rank first in the shared task. The task specification envisions a constrained The World Atlas of Language Structures (WALS) and an unconstrained track, where the constrained (Dryer and Haspelmath, 2013) is a database of systems can use only the provided WALS data, over 2,000 languages, which lists structural properties while an unconstrained system can use additional ('features') of each language, gathered from external resources, such as texts or pre-trained word reference grammars.

This paper deals with chain graphs (CGs) under the Andersson–Madigan–Perlman (AMP) interpretation. We address the problem of finding a minimal separator in an AMP CG, namely, finding a set Z of nodes that separates a given non-adjacent pair of nodes such that no proper subset of Z separates that pair. We analyze several versions of this problem and offer polynomial time algorithms for each. These include finding a minimal separator from a restricted set of nodes, finding a minimal separator for two given disjoint sets, and testing whether a given separator is minimal. To address the problem of learning the structure of AMP CGs from data, we show that the PC-like algorithm is order dependent, in the sense that the output can depend on the order in which the variables are given. We propose several modifications of the PC-like algorithm that remove part or all of this order-dependence. We also extend the decomposition-based approach for learning Bayesian networks (BNs) to learn AMP CGs, which include BNs as a special case, under the faithfulness assumption. We prove the correctness of our extension using the minimal separator results. Using standard benchmarks and synthetically generated models and data in our experiments demonstrate the competitive performance of our decomposition-based method, called LCD-AMP, in comparison with the (modified versions of) PC-like algorithm. The LCD-AMP algorithm usually outperforms the PC-like algorithm, and our modifications of the PC-like algorithm learn structures that are more similar to the underlying ground truth graphs than the original PC-like algorithm, especially in high-dimensional settings. In particular, we empirically show that the results of both algorithms are more accurate and stabler when the sample size is reasonably large and the underlying graph is sparse

Investigating real-world systems and phenomena typically requires complex models that involve a large number of parameters. Even with sizeable amount of observation data, the high complexity of the model may render accurate parameter estimation impossible. While finding a reliable point estimate of the parameter vector may not be possible in such a case, it may be possible to identify the parameter ranges based on the available data and/or prior system knowledge, or in a more general setting, we may assume a joint distribution of the model parameters. Since different parameter values are possible, this gives rise to an uncertainty class of all possible models [1, 2]. Furthermore, this naturally places the model in a Bayesian framework, where the likelihood of every possible model in the uncertainty class is described by a prior that could be constructed from prior system knowledge and existing data [3, 4]. Given an uncertain model and its uncertainty class, how can one mathematically quantify the amount of uncertainty present in the model? Common approaches include estimating the variance or entropy of the uncertain parameters, as they both provide a simple and intuitive measure of the model uncertainty. However, they both have a critical downside from a practical perspective. In practical applications that involve mathematical modeling of a complex system, one cares about the model as it can serve as a vehicle for designing an effective operator (i.e., controller, classifier, filter) that can act on the system of interest or the data produced therefrom.

Ensembles of geophysical models improve prediction accuracy and express uncertainties. We develop a novel data-driven ensembling strategy for combining geophysical models using Bayesian Neural Networks, which infers spatiotemporally varying model weights and bias, while accounting for heteroscedastic uncertainties in the observations. This produces more accurate and uncertaintyaware predictions without sacrificing interpretability. Applied to the prediction of total column ozone from an ensemble of 15 chemistry-climate models, we find that the Bayesian neural network ensemble (BayNNE) outperforms existing methods for ensembling physical models, achieving a 49.4% reduction in RMSE for temporal extrapolation, and a 67.4% reduction in RMSE for polar data voids, compared to a weighted mean. Uncertainty is also well-characterized, with 91.9% of the data points in our extrapolation validation dataset lying within 2 standard deviations and 98.9% within 3 standard deviations.