Prediction is critical for decision-making under uncertainty and lends validity to statistical inference. With targeted prediction, the goal is to optimize predictions for specific decision tasks of interest, which we represent via functionals. Although classical decision analysis extracts predictions from a Bayesian model, these predictions are often difficult to interpret and slow to compute. Instead, we design a class of parametrized actions for Bayesian decision analysis that produce optimal, scalable, and simple targeted predictions. For a wide variety of action parametrizations and loss functions--including linear actions with sparsity constraints for targeted variable selection--we derive a convenient representation of the optimal targeted prediction that yields efficient and interpretable solutions. Customized out-of-sample predictive metrics are developed to evaluate and compare among targeted predictors. Through careful use of the posterior predictive distribution, we introduce a procedure that identifies a set of near-optimal, or acceptable targeted predictors, which provide unique insights into the features and level of complexity needed for accurate targeted prediction. Simulations demonstrate excellent prediction, estimation, and variable selection capabilities. Targeted predictions are constructed for physical activity data from the National Health and Nutrition Examination Survey (NHANES) to better predict and understand the characteristics of intraday physical activity.

One of the main approaches for causal structure learning is constraint-based methods. These methods are particularly valued as they are guaranteed to asymptotically find a structure which is statistically equivalent to the ground truth. However, they may require exponentially large number of conditional independence (CI) tests in the number of variables of the system. In this paper, we propose a novel recursive constraint-based method for causal structure learning. The key idea of the proposed approach is to recursively use Markov blanket information in order to identify a variable that can be removed from the set of variables without changing the statistical relations among the remaining variables. Once such a variable is found, its neighbors are identified, the removable variable is removed, and the Markov blanket information of the remaining variables is updated. Our proposed approach reduces the required number of conditional independence tests for structure learning compared to the state of the art. We also provide a lower bound on the number of CI tests required by any constraint-based method. Comparing this lower bound to our achievable bound demonstrates the efficiency of our approach. We evaluate and compare the performance of the proposed method on both synthetic and real world structures against the state of the art.

Animals are equipped with a rich innate repertoire of sensory, behavioral and motor skills, which allows them to interact with the world immediately after birth. At the same time, many behaviors are highly adaptive and can be tailored to specific environments by means of learning. In this work, we use mathematical analysis and the framework of meta-learning (or'learning to learn') to answer when it is beneficial to learn such an adaptive strategy and when to hard-code a heuristic behavior. We find that the interplay of ecological uncertainty, task complexity and the agents' lifetime has crucial effects on the meta-learned amortized Bayesian inference performed by an agent. There exist two regimes: One in which metalearning yields a learning algorithm that implements task-dependent informationintegration and a second regime in which meta-learning imprints a heuristic or'hard-coded' behavior. Further analysis reveals that nonadaptive behaviors are not only optimal for aspects of the environment that are stable across individuals, but also in situations where an adaptation to the environment would in fact be highly beneficial, but could not be done quickly enough to be exploited within the remaining lifetime. Hard-coded behaviors should hence not only be those that always work, but also those that are too complex to be learned within a reasonable time frame. The'nature versus nurture' debate (e.g., Mutti et al., 1996; Tabery, 2014) - the question which aspects of behavior are'hard-coded' by evolution, and which are learned from experience - is one of the oldest and most controversial debates in biology.

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.

Automated scheduling is potentially a very useful tool for facilitating efficient, intuitive interactions between a robot and a human teammate. However, a current gapin automated scheduling is that it is not well understood how to best represent the timing uncertainty that human teammates introduce. This paper attempts to address this gap by designing an online human-robot collaborative packaging game that we use to build a model of human timing uncertainty from a population of crowd-workers. We conclude that heavy-tailed distributions are the best models of human temporal uncertainty, with a Log-Normal distribution achieving the best fit to our experimental data. We discuss how these results along with our collaborative online game will inform and facilitate future explorations into scheduling for improved human-robot fluency.

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.

Set prediction is about learning to predict a collection of unordered variables with unknown interrelations. Training such models with set losses imposes the structure of a metric space over sets. We focus on stochastic and underdefined cases, where an incorrectly chosen loss function leads to implausible predictions. Example tasks include conditional point-cloud reconstruction and predicting future states of molecules. In this paper, we propose an alternative to training via set losses by viewing learning as conditional density estimation. Our learning framework fits deep energy-based models and approximates the intractable likelihood with gradient-guided sampling. Furthermore, we propose a stochastically augmented prediction algorithm that enables multiple predictions, reflecting the possible variations in the target set. We empirically demonstrate on a variety of datasets the capability to learn multi-modal densities and produce multiple plausible predictions. Our approach is competitive with previous set prediction models on standard benchmarks. More importantly, it extends the family of addressable tasks beyond those that have unambiguous predictions.