Machine and deep learning have grown in popularity and use in biological research over the last decade but still present challenges in interpretability of the fitted model. The development and use of metrics to determine features driving predictions and increase model i nterpretability continues to be an open area of research. We investigate the use of Shapley Additive Explanations (SHAP) on a multi - view deep learning model applied to multi - omics data for the purposes of identifying biomolecules of interest . Rankings of features via these attribution methods are compared across various architectures to evaluate consistency of the method. We perform multiple computational experiments to assess the robustness of SHAP and investigate modeling approaches and diagnostics to increase and measure the reliability of the identification of important features. Accuracy of a random - forest model fit on subsets of features selected as being most influential as well as clustering quality using o nly these features are used as a measure of enullectiveness of the attribution method. Our findings indicate that the rankings of features resulting from SHAP are sensitive to the choice of architecture as well as dinullerent random initializations of weights, suggesting caution when u sing attribution methods on multi - view deep learning models applied to multi - omics data. We present a n alternative, simple method to assess the robustness of identification of important biomolecules.

We propose dpmm, an open-source library for synthetic data generation with Differentially Private (DP) guarantees. It includes three popular marginal models -- PrivBayes, MST, and AIM -- that achieve superior utility and offer richer functionality compared to alternative implementations. Additionally, we adopt best practices to provide end-to-end DP guarantees and address well-known DP-related vulnerabilities. Our goal is to accommodate a wide audience with easy-to-install, highly customizable, and robust model implementations. Our codebase is available from https://github.com/sassoftware/dpmm.

We consider linear non-Gaussian structural equation models that involve latent confounding. In this setting, the causal structure is identifiable, but, in general, it is not possible to identify the specific causal effects. Instead, a finite number of different causal effects result in the same observational distribution. Most existing algorithms for identifying these causal effects use overcomplete independent component analysis (ICA), which often suffers from convergence to local optima. Furthermore, the number of latent variables must be known a priori. To address these issues, we propose an algorithm that operates recursively rather than using overcomplete ICA. The algorithm first infers a source, estimates the effect of the source and its latent parents on their descendants, and then eliminates their influence from the data. For both source identification and effect size estimation, we use rank conditions on matrices formed from higher-order cumulants. We prove asymptotic correctness under the mild assumption that locally, the number of latent variables never exceeds the number of observed variables. Simulation studies demonstrate that our method achieves comparable performance to overcomplete ICA even though it does not know the number of latents in advance.

The Copula is widely used to describe the relationship between the marginal distribution and joint distribution of random variables. The estimation of high-dimensional Copula is difficult, and most existing solutions rely either on simplified assumptions or on complicating recursive decompositions. Therefore, people still hope to obtain a generic Copula estimation method with both universality and simplicity. To reach this goal, a novel neural network-based method (named Neural Copula) is proposed in this paper. In this method, a hierarchical unsupervised neural network is constructed to estimate the marginal distribution function and the Copula function by solving differential equations. In the training program, various constraints are imposed on both the neural network and its derivatives. The Copula estimated by the proposed method is smooth and has an analytic expression. The effectiveness of the proposed method is evaluated on both real-world datasets and complex numerical simulations. Experimental results show that Neural Copula's fitting quality for complex distributions is much better than classical methods. The relevant code for the experiments is available on GitHub. (We encourage the reader to run the program for a better understanding of the proposed method).

We introduce an approach to counterfactual inference based on merging information from multiple datasets. We consider a causal reformulation of the statistical marginal problem: given a collection of marginal structural causal models (SCMs) over distinct but overlapping sets of variables, determine the set of joint SCMs that are counterfactually consistent with the marginal ones. We formalise this approach for categorical SCMs using the response function formulation and show that it reduces the space of allowed marginal and joint SCMs. Our work thus highlights a new mode of falsifiability through additional variables, in contrast to the statistical one via additional data.

We introduce an improved variational autoencoder (VAE) for text modeling with topic information explicitly modeled as a Dirichlet latent variable. By providing the proposed model topic awareness, it is more superior at reconstructing input texts. Furthermore, due to the inherent interactions between the newly introduced Dirichlet variable and the conventional multivariate Gaussian variable, the model is less prone to KL divergence vanishing. We derive the variational lower bound for the new model and conduct experiments on four different data sets. The results show that the proposed model is superior at text reconstruction across the latent space and classifications on learned representations have higher test accuracies.

Bayesian network models with latent variables are widely used in statistics and machine learning. In this paper we provide a complete algebraic characterization of Bayesian network models with latent variables when the observed variables are discrete and no assumption is made about the state-space of the latent variables. We show that it is algebraically equivalent to the so-called nested Markov model, meaning that the two are the same up to inequality constraints on the joint probabilities. In particular these two models have the same dimension. The nested Markov model is therefore the best possible description of the latent variable model that avoids consideration of inequalities, which are extremely complicated in general. A consequence of this is that the constraint finding algorithm of Tian and Pearl (UAI 2002, pp519-527) is complete for finding equality constraints. Latent variable models suffer from difficulties of unidentifiable parameters and non-regular asymptotics; in contrast the nested Markov model is fully identifiable, represents a curved exponential family of known dimension, and can easily be fitted using an explicit parameterization.

As cloud computing gains in popularity, understanding the patterns and structure of its loads is increasingly important in order to drive effective resource allocation, scheduling and pricing decisions. These efficiency increases are then associated with a reduction in the data center environmental footprint. Existing models have only treated a single resource type, such as CPU, or memory, at a time. We offer a sophisticated machine learning approach to capture the joint-distribution. We capture the relationship among multiple resources by carefully fitting both the marginal distributions of each resource type as well as the non-linear structure of their correlation via a copula distribution. We investigate several choices for both models by studying a public data set of Google data-center usage. We show the Burr XII distribution to be a particularly effective choice for modeling the marginals and the Frank copula to be the best choice for stitching these together into a joint distribution. Our approach offers a significant fidelity improvement and generalizes directly to higher dimensions. In use, this improvement will translate directly to reductions in energy consumption.

We are developing a general framework for using learned Bayesian models for decision-theoretic control of search and reasoningalgorithms. We illustrate the approach on the specific task of controlling both general and domain-specific solvers on a hard class of structured constraint satisfaction problems. A successful strategyfor reducing the high (and even infinite) variance in running time typically exhibited by backtracking search algorithms is to cut off and restart the search if a solution is not found within a certainamount of time. Previous work on restart strategies have employed fixed cut off values. We show how to create a dynamic cut off strategy by learning a Bayesian model that predicts the ultimate length of a trial based on observing the early behavior of the search algorithm. Furthermore, we describe the general conditions under which a dynamic restart strategy can outperform the theoretically optimal fixed strategy.

We present a new approach to credal nets, which are graphical models that generalise Bayesian nets to imprecise probability. Instead of applying the commonly used notion of strong independence, we replace it by the weaker notion of epistemic irrelevance. We show how assessments of epistemic irrelevance allow us to construct a global model out of given local uncertainty models and mention some useful properties. The main results and proofs are presented using the language of sets of desirable gambles, which provides a very general and expressive way of representing imprecise probability models.