Message passing on a factor graph is a powerful paradigm for the coding of approximate inference algorithms for arbitrarily large graphical models. The notion of a factor graph fragment allows for compartmentalization of algebra and computer code. We show that the Inverse G-Wishart family of distributions enables fundamental variational message passing factor graph fragments to be expressed elegantly and succinctly. Such fragments arise in models for which approximate inference concerning covariance matrix or variance parameters is made, and are ubiquitous in contemporary statistics and machine learning. Keywords: Approximate Bayesian inference; G-Wishart distribution; mean field variational Bayes; scalable statistical methodology.

We present the Additive Poisson Process (APP), a novel framework that can model the higher-order interaction effects of the intensity functions in stochastic processes using lower dimensional projections. Our model combines the techniques in information geometry to model higher-order interactions on a statistical manifold and in generalized additive models to use lower-dimensional projections to overcome the effects from the curse of dimensionality. Our approach solves a convex optimization problem by minimizing the KL divergence from a sample distribution in lower dimensional projections to the distribution modeled by an intensity function in the stochastic process. Our empirical results show that our model is able to use samples observed in the lower dimensional space to estimate the higher-order intensity function with extremely sparse observations.

We propose an approach to estimate the effect of multiple simultaneous interventions in the presence of hidden confounders. To overcome the problem of hidden confounding, we consider the setting where we have access to not only the observational data but also sets of single-variable interventions in which each of the treatment variables is intervened on separately. We prove identifiability under the assumption that the data is generated from a nonlinear continuous structural causal model with additive Gaussian noise. In addition, we propose a simple parameter estimation method by pooling all the data from different regimes and jointly maximizing the combined likelihood. We also conduct comprehensive experiments to verify the identifiability result as well as to compare the performance of our approach against a baseline on both synthetic and real-world data.

Explainable AI (XAI) aims to provide interpretations for predictions made by learning machines, such as deep neural networks, in order to make the machines more transparent for the user and furthermore trustworthy also for applications in e.g. safety-critical areas. So far, however, no methods for quantifying uncertainties of explanations have been conceived, which is problematic in domains where a high confidence in explanations is a prerequisite. We therefore contribute by proposing a new framework that allows to convert any arbitrary explanation method for neural networks into an explanation method for Bayesian neural networks, with an in-built modeling of uncertainties. Within the Bayesian framework a network's weights follow a distribution that extends standard single explanation scores and heatmaps to distributions thereof, in this manner translating the intrinsic network model uncertainties into a quantification of explanation uncertainties. This allows us for the first time to carve out uncertainties associated with a model explanation and subsequently gauge the appropriate level of explanation confidence for a user (using percentiles). We demonstrate the effectiveness and usefulness of our approach extensively in various experiments, both qualitatively and quantitatively.

The problem of selecting a small, yet high quality subset of patterns from a larger collection of itemsets has recently attracted lot of research. Here we discuss an approach to this problem using the notion of decomposable families of itemsets. Such itemset families define a probabilistic model for the data from which the original collection of itemsets has been derived from. Furthermore, they induce a special tree structure, called a junction tree, familiar from the theory of Markov Random Fields. The method has several advantages. The junction trees provide an intuitive representation of the mining results. From the computational point of view, the model provides leverage for problems that could be intractable using the entire collection of itemsets. We provide an efficient algorithm to build decomposable itemset families, and give an application example with frequency bound querying using the model. Empirical results show that our algorithm yields high quality results.

Differential privacy (DP) is a compelling privacy definition that explains the privacy-utility tradeoff via formal, provable guarantees. Inspired by recent progress toward general-purpose data release algorithms, we propose a private sketch, or small summary of the dataset, that supports a multitude of machine learning tasks including regression, classification, density estimation, near-neighbor search, and more. Our sketch consists of randomized contingency tables that are indexed with locality-sensitive hashing and constructed with an efficient one-pass algorithm. We prove competitive error bounds for DP kernel density estimation. Existing methods for DP kernel density estimation scale poorly, often exponentially slower with an increase in dimensions. In contrast, our sketch can quickly run on large, high-dimensional datasets in a single pass. Exhaustive experiments show that our generic sketch delivers a similar privacy-utility tradeoff when compared to existing DP methods at a fraction of the computation cost. We expect that our sketch will enable differential privacy in distributed, large-scale machine learning settings.

Gaussian process regression is a popular Bayesian framework for surrogate modeling of expensive data sources. As part of a broader effort in scientific machine learning, many recent works have incorporated physical constraints or other a priori information within Gaussian process regression to supplement limited data and regularize the behavior of the model. We provide an overview and survey of several classes of Gaussian process constraints, including positivity or bound constraints, monotonicity and convexity constraints, differential equation constraints provided by linear PDEs, and boundary condition constraints. We compare the strategies behind each approach as well as the differences in implementation, concluding with a discussion of the computational challenges introduced by constraints.

The task of subgroup discovery (SD) is to find interpretable descriptions of subsets of a dataset that stand out with respect to a target attribute. To address the problem of mining large numbers of redundant subgroups, subgroup set discovery (SSD) has been proposed. State-of-the-art SSD methods have their limitations though, as they typically heavily rely on heuristics and/or user-chosen hyperparameters. We propose a dispersion-aware problem formulation for subgroup set discovery that is based on the minimum description length (MDL) principle and subgroup lists. We argue that the best subgroup list is the one that best summarizes the data given the overall distribution of the target. We restrict our focus to a single numeric target variable and show that our formalization coincides with an existing quality measure when finding a single subgroup, but that-in addition-it allows to trade off subgroup quality with the complexity of the subgroup. We next propose SSD++, a heuristic algorithm for which we empirically demonstrate that it returns outstanding subgroup lists: non-redundant sets of compact subgroups that stand out by having strongly deviating means and small spread.

Model noise is known to have detrimental effects on neural networks, such as training instability and predictive distributions with non-calibrated uncertainty properties. These factors set bottlenecks on the expressive potential of Neural Stochastic Differential Equations (NSDEs), a model family that employs neural nets on both drift and diffusion functions. We introduce a novel algorithm that solves a generic NSDE using only deterministic approximation methods. Given a discretization, we estimate the marginal distribution of the It\^{o} process implied by the NSDE using a recursive scheme to propagate deterministic approximations of the statistical moments across time steps. The proposed algorithm comes with theoretical guarantees on numerical stability and convergence to the true solution, enabling its computational use for robust, accurate, and efficient prediction of long sequences. We observe our novel algorithm to behave interpretably on synthetic setups and to improve the state of the art on two challenging real-world tasks.

When images are statistically described by a generative model we can use this information to develop optimum techniques for various image restoration problems as inpainting, super-resolution, image coloring, generative model inversion, etc. With the help of the generative model it is possible to formulate, in a natural way, these restoration problems as Statistical estimation problems. Our approach, by combining maximum a-posteriori probability with maximum likelihood estimation, is capable of restoring images that are distorted by transformations even when the latter contain unknown parameters. The resulting optimization is completely defined with no parameters requiring tuning. This must be compared with the current state of the art which requires exact knowledge of the transformations and contains regularizer terms with weights that must be properly defined. Finally, we must mention that we extend our method to accommodate mixtures of multiple images where each image is described by its own generative model and we are able of successfully separating each participating image from a single mixture.