Service robots are integrating more and more into our daily lives to help us with various tasks. In such environments, robots frequently face new objects while working in the environment and need to learn them in an open-ended fashion. Furthermore, such robots must be able to recognize a wide range of object categories. In this paper, we present a lifelong ensemble learning approach based on multiple representations to address the few-shot object recognition problem. In particular, we form ensemble methods based on deep representations and handcrafted 3D shape descriptors. To facilitate lifelong learning, each approach is equipped with a memory unit for storing and retrieving object information instantly. The proposed model is suitable for open-ended learning scenarios where the number of 3D object categories is not fixed and can grow over time. We have performed extensive sets of experiments to assess the performance of the proposed approach in offline, and open-ended scenarios. For the evaluation purpose, in addition to real object datasets, we generate a large synthetic household objects dataset consisting of 27000 views of 90 objects. Experimental results demonstrate the effectiveness of the proposed method on online few-shot 3D object recognition tasks, as well as its superior performance over the state-of-the-art open-ended learning approaches. Furthermore, our results show that while ensemble learning is modestly beneficial in offline settings, it is significantly beneficial in lifelong few-shot learning situations. Additionally, we demonstrated the effectiveness of our approach in both simulated and real-robot settings, where the robot rapidly learned new categories from limited examples.

This work introduces a novel principle for disentanglement we call mechanism sparsity regularization, which applies when the latent factors of interest depend sparsely on observed auxiliary variables and/or past latent factors. We propose a representation learning method that induces disentanglement by simultaneously learning the latent factors and the sparse causal graphical model that explains them. We develop a nonparametric identifiability theory that formalizes this principle and shows that the latent factors can be recovered by regularizing the learned causal graph to be sparse. More precisely, we show identifiablity up to a novel equivalence relation we call "consistency", which allows some latent factors to remain entangled (hence the term partial disentanglement). To describe the structure of this entanglement, we introduce the notions of entanglement graphs and graph preserving functions. We further provide a graphical criterion which guarantees complete disentanglement, that is identifiability up to permutations and element-wise transformations. We demonstrate the scope of the mechanism sparsity principle as well as the assumptions it relies on with several worked out examples. For instance, the framework shows how one can leverage multi-node interventions with unknown targets on the latent factors to disentangle them. We further draw connections between our nonparametric results and the now popular exponential family assumption. Lastly, we propose an estimation procedure based on variational autoencoders and a sparsity constraint and demonstrate it on various synthetic datasets. This work is meant to be a significantly extended version of Lachapelle et al. (2022).

In this work, we propose an original method for aggregating multiple clustering coming from different sources of information. Each partition is encoded by a co-membership matrix between observations. Our approach uses a mixture of multilayer Stochastic Block Models (SBM) to group co-membership matrices with similar information into components and to partition observations into different clusters, taking into account their specificities within the components. The identifiability of the model parameters is established and a variational Bayesian EM algorithm is proposed for the estimation of these parameters. The Bayesian framework allows for selecting an optimal number of clusters and components. The proposed approach is compared using synthetic data with consensus clustering and tensor-based algorithms for community detection in large-scale complex networks. Finally, the method is utilized to analyze global food trading networks, leading to structures of interest.

Federated Learning (FL) involves training a model over a dataset distributed among clients, with the constraint that each client's dataset is localized and possibly heterogeneous. In FL, small and noisy datasets are common, highlighting the need for well-calibrated models that represent the uncertainty of predictions. The closest FL techniques to achieving such goals are the Bayesian FL methods which collect parameter samples from local posteriors, and aggregate them to approximate the global posterior. To improve scalability for larger models, one common Bayesian approach is to approximate the global predictive posterior by multiplying local predictive posteriors. In this work, we demonstrate that this method gives systematically overconfident predictions, and we remedy this by proposing $\beta$-Predictive Bayes, a Bayesian FL algorithm that interpolates between a mixture and product of the predictive posteriors, using a tunable parameter $\beta$. This parameter is tuned to improve the global ensemble's calibration, before it is distilled to a single model. Our method is evaluated on a variety of regression and classification datasets to demonstrate its superiority in calibration to other baselines, even as data heterogeneity increases. Code available at https://github.com/hasanmohsin/betaPredBayesFL

Consider the problem of estimating a random variable $X$ from noisy observations $Y = X+ Z$, where $Z$ is standard normal, under the $L^1$ fidelity criterion. It is well known that the optimal Bayesian estimator in this setting is the conditional median. This work shows that the only prior distribution on $X$ that induces linearity in the conditional median is Gaussian. Along the way, several other results are presented. In particular, it is demonstrated that if the conditional distribution $P_{X|Y=y}$ is symmetric for all $y$, then $X$ must follow a Gaussian distribution. Additionally, we consider other $L^p$ losses and observe the following phenomenon: for $p \in [1,2]$, Gaussian is the only prior distribution that induces a linear optimal Bayesian estimator, and for $p \in (2,\infty)$, infinitely many prior distributions on $X$ can induce linearity. Finally, extensions are provided to encompass noise models leading to conditional distributions from certain exponential families.

The goal of Causal Discovery is to find automated search methods for learning causal structures from observational data. In some cases all variables of the interested causal mechanism are measured, and the task is to predict the effects one measured variable has on another. In contrast, sometimes the variables of primary interest are not directly observable but instead inferred from their manifestations in the data. These are referred to as latent variables. One commonly known example is the psychological construct of intelligence, which cannot directly measured so researchers try to assess through various indicators such as IQ tests. In this case, casual discovery algorithms can uncover underlying patterns and structures to reveal the causal connections between the latent variables and between the latent and observed variables. This thesis focuses on two questions in causal discovery: providing an alternative definition of k-Triangle Faithfulness that (i) is weaker than strong faithfulness when applied to the Gaussian family of distributions, (ii) can be applied to non-Gaussian families of distributions, and (iii) under the assumption that the modified version of Strong Faithfulness holds, can be used to show the uniform consistency of a modified causal discovery algorithm; relaxing the sufficiency assumption to learn causal structures with latent variables. Given the importance of inferring cause-and-effect relationships for understanding and forecasting complex systems, the work in this thesis of relaxing various simplification assumptions is expected to extend the causal discovery method to be applicable in a wider range with diversified causal mechanism and statistical phenomena.

Observational cohort studies are increasingly being used for comparative effectiveness research to assess the safety of therapeutics. Recently, various doubly robust methods have been proposed for average treatment effect estimation by combining the treatment model and the outcome model via different vehicles, such as matching, weighting, and regression. The key advantage of doubly robust estimators is that they require either the treatment model or the outcome model to be correctly specified to obtain a consistent estimator of average treatment effects, and therefore lead to a more accurate and often more precise inference. However, little work has been done to understand how doubly robust estimators differ due to their unique strategies of using the treatment and outcome models and how machine learning techniques can be combined to boost their performance. Here we examine multiple popular doubly robust methods and compare their performance using different treatment and outcome modeling via extensive simulations and a real-world application. We found that incorporating machine learning with doubly robust estimators such as the targeted maximum likelihood estimator gives the best overall performance. Practical guidance on how to apply doubly robust estimators is provided.

At its core, this thesis aims to enhance the practicality of deep learning by improving the label and training efficiency of deep learning models. To this end, we investigate data subset selection techniques, specifically active learning and active sampling, grounded in information-theoretic principles. Active learning improves label efficiency, while active sampling enhances training efficiency. Supervised deep learning models often require extensive training with labeled data. Label acquisition can be expensive and time-consuming, and training large models is resource-intensive, hindering the adoption outside academic research and ``big tech.'' Existing methods for data subset selection in deep learning often rely on heuristics or lack a principled information-theoretic foundation. In contrast, this thesis examines several objectives for data subset selection and their applications within deep learning, striving for a more principled approach inspired by information theory. We begin by disentangling epistemic and aleatoric uncertainty in single forward-pass deep neural networks, which provides helpful intuitions and insights into different forms of uncertainty and their relevance for data subset selection. We then propose and investigate various approaches for active learning and data subset selection in (Bayesian) deep learning. Finally, we relate various existing and proposed approaches to approximations of information quantities in weight or prediction space. Underpinning this work is a principled and practical notation for information-theoretic quantities that includes both random variables and observed outcomes. This thesis demonstrates the benefits of working from a unified perspective and highlights the potential impact of our contributions to the practical application of deep learning.

The Boltzmann distribution of a protein provides a roadmap to all of its functional states. Normalizing flows are a promising tool for modeling this distribution, but current methods are intractable for typical pharmacological targets; they become computationally intractable due to the size of the system, heterogeneity of intramolecular potential energy, and long-range interactions. To remedy these issues, we present a novel flow architecture that utilizes split channels and gated attention to efficiently learn the conformational distribution of proteins defined by internal coordinates. We show that by utilizing a 2-Wasserstein loss, one can smooth the transition from maximum likelihood training to energy-based training, enabling the training of Boltzmann Generators for macromolecules. We evaluate our model and training strategy on villin headpiece HP35(nle-nle), a 35-residue subdomain, and protein G, a 56-residue protein. We demonstrate that standard architectures and training strategies, such as maximum likelihood alone, fail while our novel architecture and multi-stage training strategy are able to model the conformational distributions of protein G and HP35. The structural ensemble of a protein determines its functions. The probabilities of the ground and metastable states of a protein at equilibrium for a given temperature determine the interactions of the protein with other proteins, effectors, and drugs, which are keys for pharmaceutical development. However, enumeration of the equilibrium conformations and their probabilities is infeasible. Since complete knowledge is inaccessible, we must adopt a sampling approach. Conventional approaches toward sampling the equilibrium ensemble rely on Markov-chain Monte Carlo or molecular dynamics (MD). These approaches explore the local energy landscape adjacent a starting point; however, they are limited by their inability to penetrate high energy barriers. In addition, MD simulations are expensive and scale poorly with system size.

In this manuscript, we present various proposed methods estimate the prevalence of disease, a critical prerequisite for the adequate interpretation of screening tests. To address the limitations of these approaches, which revolve primarily around their a posteriori nature, we introduce a novel method to estimate the pretest probability of disease, a priori, utilizing the Logit function from the logistic regression model. This approach is a modification of McGee's heuristic, originally designed for estimating the posttest probability of disease. In a patient presenting with $n_\theta$ signs or symptoms, the minimal bound of the pretest probability, $\phi$, can be approximated by: $\phi \approx \frac{1}{5}{ln\left[\displaystyle\prod_{\theta=1}^{i}\kappa_\theta\right]}$ where $ln$ is the natural logarithm, and $\kappa_\theta$ is the likelihood ratio associated with the sign or symptom in question.