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Connect with a Mila academic advisor and current student-researchers to learn more about Mila's community and how to join us on August 19, 31 and September 11, 2026.
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Publications
Noise covariance estimation in multi-task high-dimensional linear models
In model-based reinforcement learning, an agent can leverage a learned model to improve its way of behaving in different ways. Two prevalent… (see more) approaches are decision-time planning and background planning. In this study, we are interested in understanding under what conditions and in which settings one of these two planning styles will perform better than the other in domains that require fast responses. After viewing them through the lens of dynamic programming, we first consider the classical instantiations of these planning styles and provide theoretical results and hypotheses on which one will perform better in the pure planning, planning&learning, and transfer learning settings. We then consider the modern instantiations of these planning styles and provide hypotheses on which one will perform better in the last two of the considered settings. Lastly, we perform several illustrative experiments to empirically validate both our theoretical results and hypotheses. Overall, our findings suggest that even though decision-time planning does not perform as well as background planning in their classical instantiations, in their modern instantiations, it can perform on par or better than background planning in both the planning&learning and transfer learning settings.
Proper vertebrae formation relies on a tissue-wide oscillator called the segmentation clock. Individual cellular oscillators in the presomit… (see more)ic mesoderm are modulated by intercellular coupling and external signals, leading to the propagation of oscillatory waves of genetic expression eventually stabilizing into a static pattern. Here, we review 4 decades of biophysical models of this process, starting from the pioneering Clock and Wavefront model by Cooke and Zeeman, and the reaction–diffusion model by Meinhardt. We discuss how modern descriptions followed advances in molecular description and visualization of the process, reviewing phase models, delayed models, systems-level, and finally geometric models. We connect models to high-level aspects of embryonic development from embryonic scaling to wave propagation, up to reconstructed stem cell systems. We provide new analytical calculations and insights into classical and recent models, leading us to propose a geometric description of somitogenesis organized along two primary waves of differentiation.
There has been increasing demand for establishing privacy-preserving methodologies for modern statistics and machine learning. Differential … (see more)privacy, a mathematical notion from computer science, is a rising tool offering robust privacy guarantees. Recent work focuses primarily on developing differentially private versions of individual statistical and machine learning tasks, with nontrivial upstream pre-processing typically not incorporated. An important example is when record linkage is done prior to downstream modeling. Record linkage refers to the statistical task of linking two or more data sets of the same group of entities without a unique identifier. This probabilistic procedure brings additional uncertainty to the subsequent task. In this paper, we present two differentially private algorithms for linear regression with linked data. In particular, we propose a noisy gradient method and a sufficient statistics perturbation approach for the estimation of regression coefficients. We investigate the privacy-accuracy tradeoff by providing finite-sample error bounds for the estimators, which allows us to understand the relative contributions of linkage error, estimation error, and the cost of privacy. The variances of the estimators are also discussed. We demonstrate the performance of the proposed algorithms through simulations and an application to synthetic data.
Strong Gravitational Lensing as a Probe of Dark Matter
S. Vegetti
S. Birrer
G. Despali
C.D. Fassnacht
D. Gilman
Y. Hezaveh
L.
L. Perreault Levasseur
J.P. McKean
D.M. Powell
C.M. O'Riordan
G.
G. Vernardos
Dark matter structures within strong gravitational lens galaxies and along their line of sight leave a gravitational imprint on the multiple… (see more) images of lensed sources. Strong gravitational lensing provides, therefore, a key test of different dark matter models in a way that is independent of the baryonic content of matter structures on subgalactic scales. In this chapter, we describe how galaxy-scale strong gravitational lensing observations are sensitive to the physical nature of dark matter. We provide a historical perspective of the field, and review its current status. We discuss the challenges and advances in terms of data, treatment of systematic errors and theoretical predictions, that will enable one to deliver a stringent and robust test of different dark matter models in the near future. With the advent of the next generation of sky surveys, the number of known strong gravitational lens systems is expected to increase by several orders of magnitude. Coupled with high-resolution follow-up observations, these data will provide a key opportunity to constrain the properties of dark matter with strong gravitational lensing.
Implicitly Bayesian Prediction Rules in Deep Learning
Bruno Mlodozeniec
David M. Krueger
Richard E. Turner
The Bayesian approach leads to coherent updates of predictions under new data, which makes adhering to Bayesian principles appealing in deci… (see more)sion-making contexts. Traditionally, integrating Bayesian principles into models like deep neural networks involves setting priors on parameters and approximating posteriors. This is done despite the fact that, typically, priors on parameters reflect any prior beliefs only insofar as they dictate function space behaviour. In this paper, we rethink this approach and consider what properties characterise a prediction rule as being Bayesian. Algorithms meeting such criteria can be deemed implicitly Bayesian — they make the same predictions as some Bayesian model, without explicitly manifesting priors and posteriors. We argue this might be a more fruitful approach towards integrating Bayesian principles into deep learning. In this paper, we propose how to measure how close a general prediction rule is to being implicitly Bayesian, and empirically evaluate multiple prediction strategies using our approach. We also show theoretically that agents relying on non-implicitly Bayesian prediction rules can be easily exploited in adversarial betting settings.
2024-07-28
Proceedings of the 6th Symposium on Advances in Approximate Bayesian Inference (published)
Single-cell multi-omics data reveal complex cellular states, providing significant insights into cellular dynamics and disease. Yet, integra… (see more)tion of multi-omics data presents challenges. Some modalities have not reached the robustness or clarity of established transcriptomics. Coupled with data scarcity for less established modalities and integration intricacies, these challenges limit our ability to maximize single-cell omics benefits. We introduce scCross, a tool leveraging variational autoencoders, generative adversarial networks, and the mutual nearest neighbors (MNN) technique for modality alignment. By enabling single-cell cross-modal data generation, multi-omics data simulation, and in silico cellular perturbations, scCross enhances the utility of single-cell multi-omics studies.
The online version contains supplementary material available at 10.1186/s13059-024-03338-z.
Incident reporting and learning systems provide an opportunity to identify systemic vulnerabilities that contribute to incidents and potenti… (see more)ally degrade quality. The narrative of an incident is intended to provide a clear, easy to understand description of an incident. Unclear, incomplete or poorly organized narratives compromise the ability to learn from them. This report provides guidance for drafting effective narratives, with particular attention to the use of narratives in incident reporting and learning systems (IRLS). Examples are given that compare effective and less than effective narratives. This report is mostly directed to organizations that maintain IRLS, but also may be helpful for individuals who desire to write a useful narrative for entry into such a system. Recommendations include the following: (1) Systems should allow a one- or two-sentence, free-text synopsis of an incident without guessing at causes; (2) Information included should form a sequence of events with chronology; and (3) Reporting and learning systems should consider using the headings suggested to guide the reporter through the narrative: (a) incident occurrences and actions by role; (b) prior circumstances and actions; (c) method by which the incident was identified; (d) equipment related details if relevant; (e) recovery actions by role; (f) relevant time span between responses; (g) and how individuals affected during or immediately after incident. When possible and appropriate, supplementary information including relevant data elements should be included using numerical scales or drop-down choices outside of the narrative. Information that should not be included in the narrative includes: (a) patient health information (PHI); (b) conjecture or blame; (c) jargon abbreviations or details without specifying their significance; (d) causal analysis.