Missing values with mixed data types is a common problem in a large number of machine learning applications such as processing of surveys and in different medical applications. Recently, Gaussian copula models have been suggested as a means of performing imputation of missing values using a probabilistic framework. While the present Gaussian copula models have shown to yield state of the art performance, they have two limitations: they are based on an approximation that is fast but may be imprecise and they do not support unordered multinomial variables. We address the first limitation using direct and arbitrarily precise approximations both for model estimation and imputation by using randomized quasi-Monte Carlo procedures. The method we provide has lower errors for the estimated model parameters and the imputed values, compared to previously proposed methods. We also extend the previous Gaussian copula models to include unordered multinomial variables in addition to the present support of ordinal, binary, and continuous variables.

The 3D modelling of indoor environments and the generation of process simulations play an important role in factory and assembly planning. In brownfield planning cases existing data are often outdated and incomplete especially for older plants, which were mostly planned in 2D. Thus, current environment models cannot be generated directly on the basis of existing data and a holistic approach on how to build such a factory model in a highly automated fashion is mostly non-existent. Major steps in generating an environment model in a production plant include data collection and pre-processing, object identification as well as pose estimation. In this work, we elaborate a methodical workflow, which starts with the digitalization of large-scale indoor environments and ends with the generation of a static environment or simulation model. The object identification step is realized using a Bayesian neural network capable of point cloud segmentation. We elaborate how the information on network uncertainty generated by a Bayesian segmentation framework can be used in order to build up a more accurate environment model. The steps of data collection and point cloud segmentation as well as the resulting model accuracy are evaluated on a real-world data set collected at the assembly line of a large-scale automotive production plant. The segmentation network is further evaluated on the publicly available Stanford Large-Scale 3D Indoor Spaces data set. The Bayesian segmentation network clearly surpasses the performance of the frequentist baseline and allows us to increase the accuracy of the model placement in a simulation scene considerably.

We consider the problem of local planning in fixed-horizon Markov Decision Processes (MDPs) with a generative model under the assumption that the optimal value function lies in the span of a feature map that is accessible through the generative model. As opposed to previous work where linear realizability of all policies was assumed, we consider the significantly relaxed assumption of a single linearly realizable (deterministic) policy. A recent lower bound established that the related problem when the action-value function of the optimal policy is linearly realizable requires an exponential number of queries, either in H (the horizon of the MDP) or d (the dimension of the feature mapping). Their construction crucially relies on having an exponentially large action set. In contrast, in this work, we establish that poly$(H, d)$ learning is possible (with state value function realizability) whenever the action set is small (i.e. O(1)). In particular, we present the TensorPlan algorithm which uses poly$((dH/\delta)^A)$ queries to find a $\delta$-optimal policy relative to any deterministic policy for which the value function is linearly realizable with a parameter from a fixed radius ball around zero. This is the first algorithm to give a polynomial query complexity guarantee using only linear-realizability of a single competing value function. Whether the computation cost is similarly bounded remains an interesting open question. The upper bound is complemented by a lower bound which proves that in the infinite-horizon episodic setting, planners that achieve constant suboptimality need exponentially many queries, either in the dimension or the number of actions.

Finding the minimal structural assumptions that empower sample-efficient learning is one of the most important research directions in Reinforcement Learning (RL). This paper advances our understanding of this fundamental question by introducing a new complexity measure -- Bellman Eluder (BE) dimension. We show that the family of RL problems of low BE dimension is remarkably rich, which subsumes a vast majority of existing tractable RL problems including but not limited to tabular MDPs, linear MDPs, reactive POMDPs, low Bellman rank problems as well as low Eluder dimension problems. This paper further designs a new optimization-based algorithm -- GOLF, and reanalyzes a hypothesis elimination-based algorithm -- OLIVE (proposed in Jiang et al. (2017)). We prove that both algorithms learn the near-optimal policies of low BE dimension problems in a number of samples that is polynomial in all relevant parameters, but independent of the size of state-action space. Our regret and sample complexity results match or improve the best existing results for several well-known subclasses of low BE dimension problems.

In multi-agent reinforcement learning, the problem of learning to act is particularly difficult because the policies of co-players may be heavily conditioned on information only observed by them. On the other hand, humans readily form beliefs about the knowledge possessed by their peers and leverage beliefs to inform decision-making. Such abilities underlie individual success in a wide range of Markov games, from bluffing in Poker to conditional cooperation in the Prisoner's Dilemma, to convention-building in Bridge. Classical methods are usually not applicable to complex domains due to the intractable nature of hierarchical beliefs (i.e. beliefs of other agents' beliefs). We propose a scalable method to approximate these belief structures using recursive deep generative models, and to use the belief models to obtain representations useful to acting in complex tasks. Our agents trained with belief models outperform model-free baselines with equivalent representational capacity using common training paradigms. We also show that higher-order belief models outperform agents with lower-order models.

Probabilistic graphical models [KF09] provide a rich and unifying framework to model structured high-dimensional distributions in terms of the local dependencies between the input variables. The problem of inference in graphical models arises in many applications across scientific disciplines, see, e.g., [WJ08]. In this work, we study the inverse problem of learning graphical models from data. Various formalizations of this general learning problem have been studied during the past five decades, see, e.g., [CL68, Das97, AKN06, WRL06, AHHK12, SW12, LW12, BMS13, BGS14, Bre15, KM17], resulting in general theory and algorithms for various settings. In this work, we focus on learning Ising models [Isi25], the prototypical family of binary undirected graphical models with applications in computer vision, computational biology, and statistical physics [Li09, JEMF06, Fel04, Cha05].

Multivariate time series analysis is becoming an integral part of data analysis pipelines. Understanding the individual time point connections between covariates as well as how these connections change in time is non-trivial. To this aim, we propose a novel method that leverages on Hidden Markov Models and Gaussian Graphical Models -- Time Adaptive Gaussian Model (TAGM). Our model is a generalization of state-of-the-art methods for the inference of temporal graphical models, its formulation leverages on both aspects of these models providing better results than current methods. In particular,it performs pattern recognition by clustering data points in time; and, it finds probabilistic (and possibly causal) relationships among the observed variables. Compared to current methods for temporal network inference, it reduces the basic assumptions while still showing good inference performances.

Deep learning (DL) has gained much attention and become increasingly popular in modern data science. Computer scientists led the way in developing deep learning techniques, so the ideas and perspectives can seem alien to statisticians. Nonetheless, it is important that statisticians become involved -- many of our students need this expertise for their careers. In this paper, developed as part of a program on DL held at the Statistical and Applied Mathematical Sciences Institute, we address this culture gap and provide tips on how to teach deep learning to statistics graduate students. After some background, we list ways in which DL and statistical perspectives differ, provide a recommended syllabus that evolved from teaching two iterations of a DL graduate course, offer examples of suggested homework assignments, give an annotated list of teaching resources, and discuss DL in the context of two research areas.

Mathematical modelling of unemployment dynamics attempts to predict the probability of a job seeker finding a job as a function of time. This is typically achieved by using information in unemployment records. These records are right censored, making survival analysis a suitable approach for parameter estimation. The proposed model uses a deep artificial neural network (ANN) as a non-linear hazard function. Through embedding, high-cardinality categorical features are analysed efficiently. The posterior distribution of the ANN parameters are estimated using a variational Bayes method. The model is evaluated on a time-to-employment data set spanning from 2011 to 2020 provided by the Slovenian public employment service. It is used to determine the employment probability over time for each individual on the record. Similar models could be applied to other questions with multi-dimensional, high-cardinality categorical data including censored records. Such data is often encountered in personal records, for example in medical records.

Reinforcement learning algorithms are typically geared towards optimizing the expected return of an agent. However, in many practical applications, low variance in the return is desired to ensure the reliability of an algorithm. In this paper, we propose on-policy and off-policy actor-critic algorithms that optimize a performance criterion involving both mean and variance in the return. Previous work uses the second moment of return to estimate the variance indirectly. Instead, we use a much simpler recently proposed direct variance estimator which updates the estimates incrementally using temporal difference methods. Using the variance-penalized criterion, we guarantee the convergence of our algorithm to locally optimal policies for finite state action Markov decision processes. We demonstrate the utility of our algorithm in tabular and continuous MuJoCo domains. Our approach not only performs on par with actor-critic and prior variance-penalization baselines in terms of expected return, but also generates trajectories which have lower variance in the return.