We have seen rapid progress in the field of Artificial Intelligence (AI). If this progress continues, perhaps one day we will create powerful artificial agents. If we do so, how do we ensure that such AI agents do not go out of control? One approach is to make sure that we can switch off AI agents when they act against our interests. Put another way, we want to make sure that AI agents will defer to us.

Circular and non-flat data distributions are prevalent across diverse domains of data science, yet their specific geometric structures often remain underutilized in machine learning frameworks. A principled approach to accounting for the underlying geometry of such data is pivotal, particularly when extending statistical models, like the pervasive Gaussian distribution. In this work, we tackle those issue by focusing on the manifold of symmetric positive definite matrices, a key focus in information geometry. We introduced a non-isotropic wrapped Gaussian by leveraging the exponential map, we derive theoretical properties of this distribution and propose a maximum likelihood framework for parameter estimation. Furthermore, we reinterpret established classifiers on SPD through a probabilistic lens and introduce new classifiers based on the wrapped Gaussian model. Experiments on synthetic and real-world datasets demonstrate the robustness and flexibility of this geometry-aware distribution, underscoring its potential to advance manifold-based data analysis. This work lays the groundwork for extending classical machine learning and statistical methods to more complex and structured data.

Scientists often need to analyze the samples in a study that responded to treatment in order to refine their hypotheses and find potential causal drivers of response. Natural variation in outcomes makes teasing apart responders from non-responders a statistical inference problem. To handle latent responses, we introduce the causal two-groups (C2G) model, a causal extension of the classical two-groups model. The C2G model posits that treated samples may or may not experience an effect, according to some prior probability. We propose two empirical Bayes procedures for the causal two-groups model, one under semi-parametric conditions and another under fully nonparametric conditions. The semi-parametric model assumes additive treatment effects and is identifiable from observed data. The nonparametric model is unidentifiable, but we show it can still be used to test for response in each treated sample. We show empirically and theoretically that both methods for selecting responders control the false discovery rate at the target level with near-optimal power. We also propose two novel estimands of interest and provide a strategy for deriving estimand intervals in the unidentifiable nonparametric model. On a cancer immunotherapy dataset, the nonparametric C2G model recovers clinically-validated predictive biomarkers of both positive and negative outcomes. Code is available at https://github.com/tansey-lab/causal2groups.

Bayesian nonparametric methods are naturally suited to the problem of out-of-distribution (OOD) detection. However, these techniques have largely been eschewed in favor of simpler methods based on distances between pre-trained or learned embeddings of data points. Here we show a formal relationship between Bayesian nonparametric models and the relative Mahalanobis distance score (RMDS), a commonly used method for OOD detection. Building on this connection, we propose Bayesian nonparametric mixture models with hierarchical priors that generalize the RMDS. We evaluate these models on the OpenOOD detection benchmark and show that Bayesian nonparametric methods can improve upon existing OOD methods, especially in regimes where training classes differ in their covariance structure and where there are relatively few data points per class.

The Weak-form Estimation of Non-linear Dynamics (WENDy) algorithm is extended to accommodate systems of ordinary differential equations that are nonlinear-in-parameters (NiP). The extension rests on derived analytic expressions for a likelihood function, its gradient and its Hessian matrix. WENDy makes use of these to approximate a maximum likelihood estimator based on optimization routines suited for non-convex optimization problems. The resulting parameter estimation algorithm has better accuracy, a substantially larger domain of convergence, and is often orders of magnitude faster than the conventional output error least squares method (based on forward solvers). The WENDy.jl algorithm is efficiently implemented in Julia. We demonstrate the algorithm's ability to accommodate the weak form optimization for both additive normal and multiplicative log-normal noise, and present results on a suite of benchmark systems of ordinary differential equations. In order to demonstrate the practical benefits of our approach, we present extensive comparisons between our method and output error methods in terms of accuracy, precision, bias, and coverage.

The goal of conditional-independence-based discovery of graphical models is to find a graph that represents the independence structure of variables in a given dataset. To learn such a representation, conditional-independence-based approaches conduct a set of statistical tests that suffices to identify the graphical representation under some assumptions on the underlying distribution of the data. In this work, we highlight that due to the conciseness of the graphical representation, there are often many tests that are not used in the construction of the graph. These redundant tests have the potential to detect or sometimes correct errors in the learned model. We show that not all tests contain this additional information and that such redundant tests have to be applied with care. Precisely, we argue that particularly those conditional (in)dependence statements are interesting that follow only from graphical assumptions but do not hold for every probability distribution.

The paper introduces a notion of low rank conditional probability tables (CPTs). Overall the reviewers found the results innovative, interesting and theoretically justified. Many of the reviewers concerns were properly addressed in the rebuttal. Several reviewers stated that more empirical work could have greatly benefit the paper.

Gibbs sampling is a Markov Chain Monte Carlo sampling technique that iteratively samples variables from their conditional distributions. There are two common scan orders for the variables: random scan and systematic scan. Due to the benefits of locality in hardware, systematic scan is commonly used, even though most statistical guarantees are only for random scan. While it has been conjectured that the mixing times of random scan and systematic scan do not differ by more than a logarithmic factor, we show by counterexample that this is not the case, and we prove that that the mixing times do not differ by more than a polynomial factor under mild conditions. To prove these relative bounds, we introduce a method of augmenting the state space to study systematic scan using conductance.

We present a method for learning treewidth-bounded Bayesian networks from data sets containing thousands of variables. Bounding the treewidth of a Bayesian network greatly reduces the complexity of inferences. Yet, being a global property of the graph, it considerably increases the difficulty of the learning process. Our novel algorithm accomplishes this task, scaling both to large domains and to large treewidths. Our novel approach consistently outperforms the state of the art on experiments with up to thousands of variables.

In this work, we propose an infinite restricted Boltzmann machine (RBM), whose maximum likelihood estimation (MLE) corresponds to a constrained convex optimization. We consider the Frank-Wolfe algorithm to solve the program, which provides a sparse solution that can be interpreted as inserting a hidden unit at each iteration, so that the optimization process takes the form of a sequence of finite models of increasing complexity. As a side benefit, this can be used to easily and efficiently identify an appropriate number of hidden units during the optimization. The resulting model can also be used as an initialization for typical state-of-the-art RBM training algorithms such as contrastive divergence, leading to models with consistently higher test likelihood than random initialization.