Individualized treatment decisions can improve health outcomes, but using data to make these decisions in a reliable, precise, and generalizable way is challenging with a single dataset. Leveraging multiple randomized controlled trials allows for the combination of datasets with unconfounded treatment assignment to better estimate heterogeneous treatment effects. This paper discusses several non-parametric approaches for estimating heterogeneous treatment effects using data from multiple trials. We extend single-study methods to a scenario with multiple trials and explore their performance through a simulation study, with data generation scenarios that have differing levels of cross-trial heterogeneity. The simulations demonstrate that methods that directly allow for heterogeneity of the treatment effect across trials perform better than methods that do not, and that the choice of single-study method matters based on the functional form of the treatment effect. Finally, we discuss which methods perform well in each setting and then apply them to four randomized controlled trials to examine effect heterogeneity of treatments for major depressive disorder.

We introduce general tools for designing efficient private estimation algorithms, in the high-dimensional settings, whose statistical guarantees almost match those of the best known non-private algorithms. To illustrate our techniques, we consider two problems: recovery of stochastic block models and learning mixtures of spherical Gaussians. For the former, we present the first efficient $(\epsilon, \delta)$-differentially private algorithm for both weak recovery and exact recovery. Previously known algorithms achieving comparable guarantees required quasi-polynomial time. For the latter, we design an $(\epsilon, \delta)$-differentially private algorithm that recovers the centers of the $k$-mixture when the minimum separation is at least $ O(k^{1/t}\sqrt{t})$. For all choices of $t$, this algorithm requires sample complexity $n\geq k^{O(1)}d^{O(t)}$ and time complexity $(nd)^{O(t)}$. Prior work required minimum separation at least $O(\sqrt{k})$ as well as an explicit upper bound on the Euclidean norm of the centers.

Regularization is one of the most fundamental topics in optimization, statistics and machine learning. To get sparsity in estimating a parameter $u\in\mathbb{R}^d$, an $\ell_q$ penalty term, $\Vert u\Vert_q$, is usually added to the objective function. What is the probabilistic distribution corresponding to such $\ell_q$ penalty? What is the correct stochastic process corresponding to $\Vert u\Vert_q$ when we model functions $u\in L^q$? This is important for statistically modeling large dimensional objects, e.g. images, with penalty to preserve certainty properties, e.g. edges in the image. In this work, we generalize the $q$-exponential distribution (with density proportional to) $\exp{(- \frac{1}{2}|u|^q)}$ to a stochastic process named $Q$-exponential (Q-EP) process that corresponds to the $L_q$ regularization of functions. The key step is to specify consistent multivariate $q$-exponential distributions by choosing from a large family of elliptic contour distributions. The work is closely related to Besov process which is usually defined by the expanded series. Q-EP can be regarded as a definition of Besov process with explicit probabilistic formulation and direct control on the correlation length. From the Bayesian perspective, Q-EP provides a flexible prior on functions with sharper penalty ($q<2$) than the commonly used Gaussian process (GP). We compare GP, Besov and Q-EP in modeling functional data, reconstructing images, and solving inverse problems and demonstrate the advantage of our proposed methodology.

The estimation of categorical distributions under marginal constraints summarizing some sample from a population in the most-generalizable way is key for many machine-learning and data-driven approaches. We provide a parameter-agnostic theoretical framework that enables this task ensuring (i) that a categorical distribution of Maximum Entropy under marginal constraints always exists and (ii) that it is unique. The procedure of iterative proportional fitting (IPF) naturally estimates that distribution from any consistent set of marginal constraints directly in the space of probabilities, thus deductively identifying a least-biased characterization of the population. The theoretical framework together with IPF leads to a holistic workflow that enables modeling any class of categorical distributions solely using the phenomenological information provided.

We revisit the problem of efficiently learning the underlying parameters of Ising models from data. Current algorithmic approaches achieve essentially optimal sample complexity when given i.i.d. samples from the stationary measure and the underlying model satisfies "width" bounds on the total $\ell_1$ interaction involving each node. We show that a simple existing approach based on node-wise logistic regression provably succeeds at recovering the underlying model in several new settings where these assumptions are violated: (1) Given dynamically generated data from a wide variety of local Markov chains, like block or round-robin dynamics, logistic regression recovers the parameters with optimal sample complexity up to $\log\log n$ factors. This generalizes the specialized algorithm of Bresler, Gamarnik, and Shah [IEEE Trans. Inf. Theory'18] for structure recovery in bounded degree graphs from Glauber dynamics. (2) For the Sherrington-Kirkpatrick model of spin glasses, given $\mathsf{poly}(n)$ independent samples, logistic regression recovers the parameters in most of the known high-temperature regime via a simple reduction to weaker structural properties of the measure. This improves on recent work of Anari, Jain, Koehler, Pham, and Vuong [ArXiv'23] which gives distribution learning at higher temperature. (3) As a simple byproduct of our techniques, logistic regression achieves an exponential improvement in learning from samples in the M-regime of data considered by Dutt, Lokhov, Vuffray, and Misra [ICML'21] as well as novel guarantees for learning from the adversarial Glauber dynamics of Chin, Moitra, Mossel, and Sandon [ArXiv'23]. Our approach thus significantly generalizes the elegant analysis of Wu, Sanghavi, and Dimakis [Neurips'19] without any algorithmic modification.

With the wide adoption of machine learning techniques, requirements have evolved beyond sheer high performance, often requiring models to be trustworthy. A common approach to increase the trustworthiness of such systems is to allow them to refrain from predicting. Such a framework is known as selective prediction. While selective prediction for classification tasks has been widely analyzed, the problem of selective regression is understudied. This paper presents a novel approach to selective regression that utilizes model-agnostic non-parametric uncertainty estimation. Our proposed framework showcases superior performance compared to state-of-the-art selective regressors, as demonstrated through comprehensive benchmarking on 69 datasets. Finally, we use explainable AI techniques to gain an understanding of the drivers behind selective regression. We implement our selective regression method in the open-source Python package doubt and release the code used to reproduce our experiments.

In this article we propose a novel taming Langevin-based scheme called $\mathbf{sTULA}$ to sample from distributions with superlinearly growing log-gradient which also satisfy a Log-Sobolev inequality. We derive non-asymptotic convergence bounds in $KL$ and consequently total variation and Wasserstein-$2$ distance from the target measure. Non-asymptotic convergence guarantees are provided for the performance of the new algorithm as an optimizer. Finally, some theoretical results on isoperimertic inequalities for distributions with superlinearly growing gradients are provided. Key findings are a Log-Sobolev inequality with constant independent of the dimension, in the presence of a higher order regularization and a Poincare inequality with constant independent of temperature and dimension under a novel non-convex theoretical framework.

We consider a deep neural network estimator based on empirical risk minimization with l_1-regularization. We derive a general bound for its excess risk in regression and classification (including multiclass), and prove that it is adaptively nearly-minimax (up to log-factors) simultaneously across the entire range of various function classes.

Simply-verifiable mathematical conditions for existence, uniqueness and explicit analytical computation of minimal adversarial paths (MAP) and minimal adversarial distances (MAD) for (locally) uniquely-invertible classifiers, for generalized linear models (GLM), and for entropic AI (EAI) are formulated and proven. Practical computation of MAP and MAD, their comparison and interpretations for various classes of AI tools (for neuronal networks, boosted random forests, GLM and EAI) are demonstrated on the common synthetic benchmarks: on a double Swiss roll spiral and its extensions, as well as on the two biomedical data problems (for the health insurance claim predictions, and for the heart attack lethality classification). On biomedical applications it is demonstrated how MAP provides unique minimal patient-specific risk-mitigating interventions in the predefined subsets of accessible control variables. As formulated in the seminal paper featuring the sparks of artificial general intelligence that are shown by Chat GPT-4, in the last sentence of their paper the Microsoft Research team says that "elucidating the nature and mechanisms of AI systems such as GPT-4 is a formidable challenge that has suddenly become important and urgent" [1]. Importance of getting a better understanding of the nature and mechanisms of the AI is especially underlined by the multiple very spectacular recent examples of the so-called adversarial attacks on AI tools, when very small changes in the input data - practically non-perceptable for humans - could be used for a complete corruption of the AI classification outcomes [2].

Image Segmentation is one of the core tasks in Computer Vision and solving it often depends on modeling the image appearance data via the color distributions of each it its constituent regions. Whereas many segmentation algorithms handle the appearance models dependence using alternation or implicit methods, we propose here a new approach to directly estimate them from the image without prior information on the underlying segmentation. Our method uses local high order color statistics from the image as an input to tensor factorization-based estimator for latent variable models. This approach is able to estimate models in multiregion images and automatically output the regions proportions without prior user interaction, overcoming the drawbacks from a prior attempt to this problem. We also demonstrate the performance of our proposed method in many challenging synthetic and real imaging scenarios and show that it leads to an efficient segmentation algorithm.