Armeen Taeb

Xinwei Shen, Peter Bühlmann, Armeen Taeb

Since distribution shifts are common in real-world applications, there is a pressing need to develop prediction models that are robust against such shifts. Existing frameworks, such as empirical risk minimization or distributionally robust optimization, either lack generalizability for unseen distributions or rely on postulated distance measures. Alternatively, causality offers a data-driven and structural perspective to robust predictions. However, the assumptions necessary for causal inference can be overly stringent, and the robustness offered by such causal models often lacks flexibility. In this paper, we focus on causality-oriented robustness and propose Distributional Robustness via Invariant Gradients (DRIG), a method that exploits general noise interventions in training data for robust predictions against unseen interventions, and naturally interpolates between in-distribution prediction and causality. In a linear setting, we prove that DRIG yields predictions that are robust among a data-dependent class of distribution shifts. Furthermore, we show that our framework includes anchor regression as a special case, and that it yields prediction models that protect against more diverse perturbations. We establish finite-sample results and extend our approach to semi-supervised domain adaptation to further improve prediction performance. Finally, we empirically validate our methods on synthetic simulations and on single-cell and intensive health care datasets.

Armeen Taeb, Nicolo Ruggeri, Carina Schnuck et al.

In safety-critical applications, practitioners are reluctant to trust neural networks when no interpretable explanations are available. Many attempts to provide such explanations revolve around pixel-based attributions or use previously known concepts. In this paper we aim to provide explanations by provably identifying \emph{high-level, previously unknown ground-truth concepts}. To this end, we propose a probabilistic modeling framework to derive (C)oncept (L)earning and (P)rediction (CLAP) -- a VAE-based classifier that uses visually interpretable concepts as predictors for a simple classifier. Assuming a generative model for the ground-truth concepts, we prove that CLAP is able to identify them while attaining optimal classification accuracy. Our experiments on synthetic datasets verify that CLAP identifies distinct ground-truth concepts on synthetic datasets and yields promising results on the medical Chest X-Ray dataset.

Tong Xu, Simge Küçükyavuz, Ali Shojaie et al.

This paper studies the problem of learning Bayesian networks from continuous observational data, generated according to a linear Gaussian structural equation model. We consider an $\ell_0$-penalized maximum likelihood estimator for this problem which is known to have favorable statistical properties but is computationally challenging to solve, especially for medium-sized Bayesian networks. We propose a new coordinate descent algorithm to approximate this estimator and prove several remarkable properties of our procedure: the algorithm converges to a coordinate-wise minimum, and despite the non-convexity of the loss function, as the sample size tends to infinity, the objective value of the coordinate descent solution converges to the optimal objective value of the $\ell_0$-penalized maximum likelihood estimator. Finite-sample statistical consistency guarantees are also established. To the best of our knowledge, our proposal is the first coordinate descent procedure endowed with optimality and statistical guarantees in the context of learning Bayesian networks. Numerical experiments on synthetic and real data demonstrate that our coordinate descent method can obtain near-optimal solutions while being scalable.

Renat Sergazinov, Armeen Taeb, Irina Gaynanova

Multi-view data provides complementary information on the same set of observations, with multi-omics and multimodal sensor data being common examples. Analyzing such data typically requires distinguishing between shared (joint) and unique (individual) signal subspaces from noisy, high-dimensional measurements. Despite many proposed methods, the conditions for reliably identifying joint and individual subspaces remain unclear. We rigorously quantify these conditions, which depend on the ratio of the signal rank to the ambient dimension, principal angles between true subspaces, and noise levels. Our approach characterizes how spectrum perturbations of the product of projection matrices, derived from each view's estimated subspaces, affect subspace separation. Using these insights, we provide an easy-to-use and scalable estimation algorithm. In particular, we employ rotational bootstrap and random matrix theory to partition the observed spectrum into joint, individual, and noise subspaces. Diagnostic plots visualize this partitioning, providing practical and interpretable insights into the estimation performance. In simulations, our method estimates joint and individual subspaces more accurately than existing approaches. Applications to multi-omics data from colorectal cancer patients and nutrigenomic study of mice demonstrate improved performance in downstream predictive tasks.

Mona Azadkia, Armeen Taeb, Peter Bühlmann

We study the problem of causal structure learning with essentially no assumptions on the functional relationships and noise. We develop DAG-FOCI, a computationally fast algorithm for this setting that is based on the FOCI variable selection algorithm in~\cite{azadkia2021simple}. DAG-FOCI outputs the set of parents of a response variable of interest. We provide theoretical guarantees of our procedure when the underlying graph does not contain any (undirected) cycle containing the response variable of interest. Furthermore, in the absence of this assumption, we give a conservative guarantee against false positive causal claims when the set of parents is identifiable. We demonstrate the applicability of DAG-FOCI on simulated as well as a real dataset from computational biology~\cite{sachs2005causal}.

Armeen Taeb, Parikshit Shah, Venkat Chandrasekaran

Fitting a graphical model to a collection of random variables given sample observations is a challenging task if the observed variables are influenced by latent variables, which can induce significant confounding statistical dependencies among the observed variables. We present a new convex relaxation framework based on regularized conditional likelihood for latent-variable graphical modeling in which the conditional distribution of the observed variables conditioned on the latent variables is given by an exponential family graphical model. In comparison to previously proposed tractable methods that proceed by characterizing the marginal distribution of the observed variables, our approach is applicable in a broader range of settings as it does not require knowledge about the specific form of distribution of the latent variables and it can be specialized to yield tractable approaches to problems in which the observed data are not well-modeled as Gaussian. We demonstrate the utility and flexibility of our framework via a series of numerical experiments on synthetic as well as real data.