Non-prehensile manipulation is a crucial skill for enabling versatile robots to interact with ungraspable objects, using actions such as pushing, rolling, or tossing. However, achieving dexterous non-prehensile manipulation in robots poses significant challenges. During contact interactions, different contact modes arise such as sticking, sliding, and separation, and transitions between these contact modes lead to hybrid dynamics [1, 2, 3]. Furthermore, due to its underactuated nature, it requires long-term reasoning about contact interactions as well as reactive control to recover from mistakes and disturbances [1, 2]. The frictional interactions between the robot, the object, and the environment are difficult to model, which creates uncertainty in the behavior of the object [4, 5]. The highly uncertain nature of the underactuated frictional interactions [4, 5] make the nonprehensile manipulation problem especially sensitive to occlusions. Previous non-prehensile works assume near-perfect visual perception from external systems, providing either point-cloud [6] or pose observations [7, 8, 9, 10, 11]. However, moving towards more versatile onboard perception will make frequent occlusions unavoidable, either due to obstacles in the environment, self occlusions, or even human-induced occlusions, for instance in a human-robot collaboration setting. In this paper, we propose a learning-based system for non-prehensile manipulation that leverages tactile sensing to overcome occlusions in the visual perception.

In this work, we address the problem of controlling a classifier's accuracy at any user-specified level through selective classification, regardless of the problem's inherent difficulty. Traditional classification frameworks are designed to approximate the Bayes optimal error rate as closely as possible. However, with the growing deployment of artificial intelligence (AI) systems in automated, high-stakes decision-making, it has become critical to ensure reliable control over a classifier's accuracy and to guarantee accurate predictions for all individuals. When the underlying problem is truly difficult, as indicated by the distance between the true distributions for each decision class, achieving control over the error rate of an automated decisionmaking system may be impossible. This is particularly true when the number of potential classes is large or when the distributions of these classes are close enough, significantly increasing the difficulty of the problem. This phenomenon is illustrated in Figure 1, where the task is to classify various observations as High-Risk or Low-Risk, while maintaining an error rate below 5%. In this example, the High-Risk and Low-Risk classes are modeled as mixtures of two normal distributions with means of 2 and 1, respectively, and a shared variance of 1. The Bayes classifier is represented by the dotted line in the leftmost plot of Figure 1. In this scenario, the Bayes optimal error rate is 15.9%, significantly exceeding our target classification error of 5%.

Parametric Bayesian modeling offers a powerful and flexible toolbox for scientific data analysis. Yet the model, however detailed, may still be wrong, and this can make inferences untrustworthy. In this paper we study nonparametrically perturbed parametric (NPP) Bayesian models, in which a parametric Bayesian model is relaxed via a distortion of its likelihood. We analyze the properties of NPP models when the target of inference is the true data distribution or some functional of it, such as in causal inference. We show that NPP models can offer the robustness of nonparametric models while retaining the data efficiency of parametric models, achieving fast convergence when the parametric model is close to true. To efficiently analyze data with an NPP model, we develop a generalized Bayes procedure to approximate its posterior. We demonstrate our method by estimating causal effects of gene expression from single cell RNA sequencing data. NPP modeling offers an efficient approach to robust Bayesian inference and can be used to robustify any parametric Bayesian model.

Recent techniques in deep generative modeling have leveraged Markov generative processes to learn complex, high-dimensional probability distributions in a more structured and flexible manner [17]. By integrating Markov chain methods with deep neural architectures, these approaches aim to exploit the representational power of deep networks while maintaining a tractable and theoretically grounded training procedure. In contrast to early generative models that relied heavily on direct maximum likelihood estimation or adversarial objectives, this class of methods employs iterative stochastic transformations--often expressed as Markovian updates--to gradually refine initial noise samples into samples drawn from the desired target distribution. Diffusion and flow matching models represent two prominent classes of generative approaches that construct data samples through a sequence of continuous transformations. Diffusion models [6, 13] introduce a forward-noising and reverse-denoising process, progressively refining a simple noise distribution into a complex target distribution by learning to undo incremental noise corruption at each step.

Quantum Boltzmann machines (QBMs) are machine-learning models for both classical and quantum data. We give an operational definition of QBM learning in terms of the difference in expectation values between the model and target, taking into account the polynomial size of the data set. By using the relative entropy as a loss function this problem can be solved without encountering barren plateaus. We prove that a solution can be obtained with stochastic gradient descent using at most a polynomial number of Gibbs states. We also prove that pre-training on a subset of the QBM parameters can only lower the sample complexity bounds. In particular, we give pre-training strategies based on mean-field, Gaussian Fermionic, and geometrically local Hamiltonians. We verify these models and our theoretical findings numerically on a quantum and a classical data set. Our results establish that QBMs are promising machine learning models.

In this paper, we study learning and knowledge acquisition (LKA) of an agent about a proposition that is either true or false. We use a Bayesian approach, where the agent receives data to update his beliefs about the proposition according to a posterior distribution. The LKA is formulated in terms of active information, with data representing external or exogenous information that modifies the agent's beliefs. It is assumed that data provide details about a number of features that are relevant to the proposition. We show that this leads to a Gibbs distribution posterior, which is in maximum entropy relative to the prior, conditioned on the side constraints that the data provide in terms of the features. We demonstrate that full learning is sometimes not possible and full knowledge acquisition is never possible when the number of extracted features is too small. We also distinguish between primary learning (receiving data about features of relevance for the proposition) and secondary learning (receiving data about the learning of another agent). We argue that this type of secondary learning does not represent true knowledge acquisition. Our results have implications for statistical learning algorithms, and we claim that such algorithms do not always generate true knowledge. The theory is illustrated with several examples.

In this paper, a novel classification algorithm that is based on Data Importance (DI) reformatting and Genetic Algorithms (GA) named GADIC is proposed to overcome the issues related to the nature of data which may hinder the performance of the Machine Learning (ML) classifiers. GADIC comprises three phases which are data reformatting phase which depends on DI concept, training phase where GA is applied on the reformatted training dataset, and testing phase where the instances of the reformatted testing dataset are being averaged based on similar instances in the training dataset. GADIC is an approach that utilizes the exiting ML classifiers with involvement of data reformatting, using GA to tune the inputs, and averaging the similar instances to the unknown instance. The averaging of the instances becomes the unknown instance to be classified in the stage of testing. GADIC has been tested on five existing ML classifiers which are Support Vector Machine (SVM), K-Nearest Neighbour (KNN), Logistic Regression (LR), Decision Tree (DT), and Na\"ive Bayes (NB). All were evaluated using seven open-source UCI ML repository and Kaggle datasets which are Cleveland heart disease, Indian liver patient, Pima Indian diabetes, employee future prediction, telecom churn prediction, bank customer churn, and tech students. In terms of accuracy, the results showed that, with the exception of approximately 1% decrease in the accuracy of NB classifier in Cleveland heart disease dataset, GADIC significantly enhanced the performance of most ML classifiers using various datasets. In addition, KNN with GADIC showed the greatest performance gain when compared with other ML classifiers with GADIC followed by SVM while LR had the lowest improvement. The lowest average improvement that GADIC could achieve is 5.96%, whereas the maximum average improvement reached 16.79%.

Bayesian reinforcement learning (BRL) is a method that merges principles from Bayesian statistics and reinforcement learning to make optimal decisions in uncertain environments. Similar to other model-based RL approaches, it involves two key components: (1) Inferring the posterior distribution of the data generating process (DGP) modeling the true environment and (2) policy learning using the learned posterior. We propose to model the dynamics of the unknown environment through deep generative models assuming Markov dependence. In absence of likelihood functions for these models we train them by learning a generalized predictive-sequential (or prequential) scoring rule (SR) posterior. We use sequential Monte Carlo (SMC) samplers to draw samples from this generalized Bayesian posterior distribution. In conjunction, to achieve scalability in the high dimensional parameter space of the neural networks, we use the gradient based Markov chain Monte Carlo (MCMC) kernels within SMC. To justify the use of the prequential scoring rule posterior we prove a Bernstein-von Misses type theorem. For policy learning, we propose expected Thompson sampling (ETS) to learn the optimal policy by maximizing the expected value function with respect to the posterior distribution. This improves upon traditional Thompson sampling (TS) and its extensions which utilize only one sample drawn from the posterior distribution. This improvement is studied both theoretically and using simulation studies assuming discrete action and state-space. Finally we successfully extend our setup for a challenging problem with continuous action space without theoretical guarantees.

We consider a class of optimization problems defined by a system of linear equations with min and max operators. This class of optimization problems has been studied under restrictive conditions, such as, (C1) the halting or stability condition; (C2) the non-negative coefficients condition; (C3) the sum up to 1 condition; and (C4) the only min or only max oerator condition. Several seminal results in the literature focus on special cases. For example, turn-based stochastic games correspond to conditions C2 and C3; and Markov decision process to conditions C2, C3, and C4. However, the systematic computational complexity study of all the cases has not been explored, which we address in this work. Some highlights of our results are: with conditions C2 and C4, and with conditions C3 and C4, the problem is NP-complete, whereas with condition C1 only, the problem is in UP intersects coUP. Finally, we establish the computational complexity of the decision problem of checking the respective conditions.

In this work, we study the problem of aggregation in the context of Bayesian Federated Learning (BFL). Using an information geometric perspective, we interpret the BFL aggregation step as finding the barycenter of the trained posteriors for a pre-specified divergence metric. We study the barycenter problem for the parametric family of $\alpha$-divergences and, focusing on the standard case of independent and Gaussian distributed parameters, we recover the closed-form solution of the reverse Kullback-Leibler barycenter and develop the analytical form of the squared Wasserstein-2 barycenter. Considering a non-IID setup, where clients possess heterogeneous data, we analyze the performance of the developed algorithms against state-of-the-art (SOTA) Bayesian aggregation methods in terms of accuracy, uncertainty quantification (UQ), model calibration (MC), and fairness. Finally, we extend our analysis to the framework of Hybrid Bayesian Deep Learning (HBDL), where we study how the number of Bayesian layers in the architecture impacts the considered performance metrics. Our experimental results show that the proposed methodology presents comparable performance with the SOTA while offering a geometric interpretation of the aggregation phase.