Random partition models are widely used in Bayesian methods for various clustering tasks, such as mixture models, topic models, and community detection problems. While the number of clusters induced by random partition models has been studied extensively, another important model property regarding the balancedness of cluster sizes has been largely neglected. We formulate a framework to define and theoretically study the balancedness of exchangeable random partition models, by analyzing how a model assigns probabilities to partitions with different levels of balancedness. We demonstrate that the "rich-get-richer" characteristic of many existing popular random partition models is an inevitable consequence of two common assumptions: product-form exchangeability and projectivity. We propose a principled way to compare the balancedness of random partition models, which gives a better understanding of what model works better and what doesn't for different applications. We also introduce the "rich-get-poorer" random partition models and illustrate their application to entity resolution tasks.

In recent years there has been a growing interest in the estimation of causal effects using machine learning algorithms, particularly in the field of economics (Athey, 2018). The newly emerging synthesis of machine learning methods with causal inference has a large potential for a more comprehensive estimation of causal effects (Lechner, 2018). On the one hand, it enables a more flexible estimation of average effects which are of main interest in microeconometrics (Imbens & Wooldridge, 2009). On the other hand, it advances the estimation beyond the average effects and allows for a systematic analysis of effect heterogeneity (Athey & Imbens, 2017). Both of these aspects contribute to a better description of the causal mechanisms and thus to a possibly more efficient treatment allocation (Zhao, Zeng, Rush, & Kosorok, 2012; Kitagawa & Tetenov, 2018; Athey & Wager, 2021; Nie, Brunskill, & Wager, 2021). Hence, applied empirical researchers can greatly benefit from the usage of machine learning methods ranging from evaluation of public policies and business decisions to designing personalized interventions (Andini, Ciani, de Blasio, D'Ignazio, & Salvestrini, 2018; Bansak et al., 2018). Machine learning estimators as such are, however, primarily designed for prediction problems and thus cannot be used directly for causal inference. Therefore, new approaches for the estimation of causal parameters using machine learning emerged (see Athey & Imbens, 2019, for an overview). In particular, the development of the so-called meta-learners have received considerable attention (see e.g.

We consider offline Imitation Learning from corrupted demonstrations where a constant fraction of data can be noise or even arbitrary outliers. Classical approaches such as Behavior Cloning assumes that demonstrations are collected by an presumably optimal expert, hence may fail drastically when learning from corrupted demonstrations. We propose a novel robust algorithm by minimizing a Median-of-Means (MOM) objective which guarantees the accurate estimation of policy, even in the presence of constant fraction of outliers. Our theoretical analysis shows that our robust method in the corrupted setting enjoys nearly the same error scaling and sample complexity guarantees as the classical Behavior Cloning in the expert demonstration setting. Our experiments on continuous-control benchmarks validate that our method exhibits the predicted robustness and effectiveness, and achieves competitive results compared to existing imitation learning methods.

Reasoning about uncertainty is vital in many real-life autonomous systems. However, current state-of-the-art planning algorithms cannot either reason about uncertainty explicitly, or do so with a high computational burden. Here, we focus on making informed decisions efficiently, using reward functions that explicitly deal with uncertainty. We formulate an approximation, namely an abstract observation model, that uses an aggregation scheme to alleviate computational costs. We derive bounds on the expected information-theoretic reward function and, as a consequence, on the value function. We then propose a method to refine aggregation to achieve identical action selection with a fraction of the computational time.

Approximate Bayesian computation (ABC) is a popular likelihood-free inference method for models with intractable likelihood functions. As ABC methods usually rely on comparing summary statistics of observed and simulated data, the choice of the statistics is crucial. This choice involves a trade-off between loss of information and dimensionality reduction, and is often determined based on domain knowledge. However, handcrafting and selecting suitable statistics is a laborious task involving multiple trial-and-error steps. In this work, we introduce an active learning method for ABC statistics selection which reduces the domain expert's work considerably. By involving the experts, we are able to handle misspecified models, unlike the existing dimension reduction methods. Moreover, empirical results show better posterior estimates than with existing methods, when the simulation budget is limited.

For stochastic models with intractable likelihood functions, approximate Bayesian computation offers a way of approximating the true posterior through repeated comparisons of observations with simulated model outputs in terms of a small set of summary statistics. These statistics need to retain the information that is relevant for constraining the parameters but cancel out the noise. They can thus be seen as thermodynamic state variables, for general stochastic models. For many scientific applications, we need strictly more summary statistics than model parameters to reach a satisfactory approximation of the posterior. Therefore, we propose to use the inner dimension of deep neural network based Autoencoders as summary statistics. To create an incentive for the encoder to encode all the parameter-related information but not the noise, we give the decoder access to explicit or implicit information on the noise that has been used to generate the training data. We validate the approach empirically on two types of stochastic models.

Safe reinforcement learning (RL) aims to learn policies that satisfy certain constraints before deploying to safety-critical applications. Primal-dual as a prevalent constrained optimization framework suffers from instability issues and lacks optimality guarantees. This paper overcomes the issues from a novel probabilistic inference perspective and proposes an Expectation-Maximization style approach to learn safe policy. We show that the safe RL problem can be decomposed to 1) a convex optimization phase with a non-parametric variational distribution and 2) a supervised learning phase. We show the unique advantages of constrained variational policy optimization by proving its optimality and policy improvement stability. A wide range of experiments on continuous robotic tasks show that the proposed method achieves significantly better performance in terms of constraint satisfaction and sample efficiency than primal-dual baselines.

As a structured prediction task, scene graph generation aims to build a visually-grounded scene graph to explicitly model objects and their relationships in an input image. Currently, the mean field variational Bayesian framework is the de facto methodology used by the existing methods, in which the unconstrained inference step is often implemented by a message passing neural network. However, such formulation fails to explore other inference strategies, and largely ignores the more general constrained optimization models. In this paper, we present a constrained structure learning method, for which an explicit constrained variational inference objective is proposed. Instead of applying the ubiquitous message-passing strategy, a generic constrained optimization method - entropic mirror descent - is utilized to solve the constrained variational inference step. We validate the proposed generic model on various popular scene graph generation benchmarks and show that it outperforms the state-of-the-art methods.

In this thesis a probabilistic framework is developed and proposed for Dynamic Object Recognition in 3D Environments. A software package is developed using C++ and Python in ROS that performs the detection and tracking task. Furthermore, a novel Gaussian Process Regression (GPR) based method is developed to detect ground points in different urban scenarios of regular, sloped and rough. The ground surface behavior is assumed to only demonstrate local input-dependent smoothness. kernel's length-scales are obtained. Bayesian inference is implemented sing \textit{Maximum a Posteriori} criterion. The log-marginal likelihood function is assumed to be a multi-task objective function, to represent a whole-frame unbiased view of the ground at each frame because adjacent segments may not have similar ground structure in an uneven scene while having shared hyper-parameter values. Simulation results shows the effectiveness of the proposed method in uneven and rough scenes which outperforms similar Gaussian process based ground segmentation methods.

Statistical relational AI and probabilistic logic programming have so far mostly focused on discrete probabilistic models. The reasons for this is that one needs to provide constructs to succinctly model the independencies in such models, and also provide efficient inference. Three types of independencies are important to represent and exploit for scalable inference in hybrid models: conditional independencies elegantly modeled in Bayesian networks, context-specific independencies naturally represented by logical rules, and independencies amongst attributes of related objects in relational models succinctly expressed by combining rules. This paper introduces a hybrid probabilistic logic programming language, DC#, which integrates distributional clauses' syntax and semantics principles of Bayesian logic programs. It represents the three types of independencies qualitatively. More importantly, we also introduce the scalable inference algorithm FO-CS-LW for DC#. FO-CS-LW is a first-order extension of the context-specific likelihood weighting algorithm (CS-LW), a novel sampling method that exploits conditional independencies and context-specific independencies in ground models.