How to efficiently explore in reinforcement learning is an open problem. Many exploration algorithms employ the epistemic uncertainty of their own value predictions -- for instance to compute an exploration bonus or upper confidence bound. Unfortunately the required uncertainty is difficult to estimate in general with function approximation. We propose epistemic value estimation (EVE): a recipe that is compatible with sequential decision making and with neural network function approximators. It equips agents with a tractable posterior over all their parameters from which epistemic value uncertainty can be computed efficiently. We use the recipe to derive an epistemic Q-Learning agent and observe competitive performance on a series of benchmarks. Experiments confirm that the EVE recipe facilitates efficient exploration in hard exploration tasks.

Supervised learning problems may become ill-posed when there is a lack of information, resulting in unstable and non-unique solutions. However, instead of solely relying on regularization, initializing an informative ill-posed operator is akin to posing better questions to achieve more accurate answers. The Fredholm integral equation of the first kind (FIFK) is a reliable ill-posed operator that can integrate distributions and prior knowledge as input information. By incorporating input distributions and prior knowledge, the FIFK operator can address the limitations of using high-dimensional input distributions by semi-supervised assumptions, leading to more precise approximations of the integral operator. Additionally, the FIFK's incorporation of probabilistic principles can further enhance the accuracy and effectiveness of solutions. In cases of noisy operator equations and limited data, the FIFK's flexibility in defining problems using prior information or cross-validation with various kernel designs is especially advantageous. This capability allows for detailed problem definitions and facilitates achieving high levels of accuracy and stability in solutions. In our study, we examined the FIFK through two different approaches. Firstly, we implemented a semi-supervised assumption by using the same Fredholm operator kernel and data function kernel and incorporating unlabeled information. Secondly, we used the MSDF method, which involves selecting different kernels on both sides of the equation to define when the mapping kernel is different from the data function kernel. To assess the effectiveness of the FIFK and the proposed methods in solving ill-posed problems, we conducted experiments on a real-world dataset. Our goal was to compare the performance of these methods against the widely used least-squares method and other comparable methods.

To do so, we first demonstrate how information-theoretic quantities can be obtained for deterministic networks as an alternative to the commonly used unrealistic stochastic networks assumption. Next, we relate the VICReg objective to mutual information maximization and use it to highlight the underlying assumptions of the objective. Based on this relationship, we derive a generalization bound for VICReg, providing generalization guarantees for downstream supervised learning tasks and present new self-supervised learning methods, derived from a mutual information maximization objective, that outperform existing methods in terms of performance.

We present a novel approach to transcranial ultrasound computed tomography that utilizes normalizing flows to improve the speed of imaging and provide Bayesian uncertainty quantification. Our method combines physics-informed methods and data-driven methods to accelerate the reconstruction of the final image. We make use of a physics-informed summary statistic to incorporate the known ultrasound physics with the goal of compressing large incoming observations. This compression enables efficient training of the normalizing flow and standardizes the size of the data regardless of imaging configurations. The combinations of these methods results in fast uncertainty-aware image reconstruction that generalizes to a variety of transducer configurations. We evaluate our approach with in silico experiments and demonstrate that it can significantly improve the imaging speed while quantifying uncertainty. We validate the quality of our image reconstructions by comparing against the traditional physics-only method and also verify that our provided uncertainty is calibrated with the error.

Under stringent model type and variable distribution assumptions, differentiable score-based causal discovery methods learn a directed acyclic graph (DAG) from observational data by evaluating candidate graphs over an average score function. Despite great success in low-dimensional linear systems, it has been observed that these approaches overly exploit easier-to-fit samples, thus inevitably learning spurious edges. Worse still, the common homogeneity assumption can be easily violated, due to the widespread existence of heterogeneous data in the real world, resulting in performance vulnerability when noise distributions vary. We propose a simple yet effective model-agnostic framework to boost causal discovery performance by dynamically learning the adaptive weights for the Reweighted Score function, ReScore for short, where the weights tailor quantitatively to the importance degree of each sample. Intuitively, we leverage the bilevel optimization scheme to alternately train a standard DAG learner and reweight samples -- that is, upweight the samples the learner fails to fit and downweight the samples that the learner easily extracts the spurious information from. Extensive experiments on both synthetic and real-world datasets are carried out to validate the effectiveness of ReScore. We observe consistent and significant boosts in structure learning performance. Furthermore, we visualize that ReScore concurrently mitigates the influence of spurious edges and generalizes to heterogeneous data. Finally, we perform the theoretical analysis to guarantee the structure identifiability and the weight adaptive properties of ReScore in linear systems. Learning causal structure from purely observational data (i.e., causal discovery) is a fundamental but daunting task (Chickering et al., 2004; Shen et al., 2020). It strives to identify causal relationships between variables and encode the conditional independence as a directed acyclic graph (DAG).

For more than half a century, vibratory bowl feeders have been the standard in automated assembly for singulation, orientation, and manipulation of small parts. Unfortunately, these feeders are expensive, noisy, and highly specialized on a single part design bases. We consider an alternative device and learning control method for singulation, orientation, and manipulation by means of seven fixed-position variable-energy solenoid impulse actuators located beneath a semi-rigid part supporting surface. Using computer vision to provide part pose information, we tested various machine learning (ML) algorithms to generate a control policy that selects the optimal actuator and actuation energy. Our manipulation test object is a 6-sided craps-style die. Using the most suitable ML algorithm, we were able to flip the die to any desired face 30.4\% of the time with a single impulse, and 51.3\% with two chosen impulses, versus a random policy succeeding 5.1\% of the time (that is, a randomly chosen impulse delivered by a randomly chosen solenoid).

Deep neural networks can learn powerful prior probability models for images, as evidenced by the high-quality generations obtained with recent score-based diffusion methods. But the means by which these networks capture complex global statistical structure, apparently without suffering from the curse of dimensionality, remain a mystery. To study this, we incorporate diffusion methods into a multi-scale decomposition, reducing dimensionality by assuming a stationary local Markov model for wavelet coefficients conditioned on coarser-scale coefficients. We instantiate this model using convolutional neural networks (CNNs) with local receptive fields, which enforce both the stationarity and Markov properties. Global structures are captured using a CNN with receptive fields covering the entire (but small) low-pass image. We test this model on a dataset of face images, which are highly non-stationary and contain large-scale geometric structures. Remarkably, denoising, super-resolution, and image synthesis results all demonstrate that these structures can be captured with significantly smaller conditioning neighborhoods than required by a Markov model implemented in the pixel domain. Our results show that score estimation for large complex images can be reduced to low-dimensional Markov conditional models across scales, alleviating the curse of dimensionality. Deep neural networks (DNNs) have produced dramatic advances in synthesizing complex images and solving inverse problems, all of which rely (at least implicitly) on prior probability models.

Traditional models of opinion dynamics provide a simple approach to understanding human behavior in basic social scenarios. However, when it comes to issues such as polarization and extremism, we require a more nuanced understanding of human biases and cognitive tendencies. In this paper, we propose an approach to modeling opinion dynamics by integrating mental models and assumptions of individuals agents using Bayesian-inspired methods. By exploring the relationship between human rationality and Bayesian theory, we demonstrate the efficacy of these methods in describing how opinions evolve. Our analysis leverages the Continuous Opinions and Discrete Actions (CODA) model, applying Bayesian-inspired rules to account for key human behaviors such as confirmation bias, motivated reasoning, and our reluctance to change opinions. Through this, we obtain update rules that offer deeper insights into the dynamics of extreme opinions. Our work sheds light on the role of human biases in shaping opinion dynamics and highlights the potential of Bayesian-inspired modeling to provide more accurate predictions of real-world scenarios. Keywords: Opinion dynamics, Bayesian methods, Cognition, CODA, Agent-based models

We study the Bayesian regret of the renowned Thompson Sampling algorithm in contextual bandits with binary losses and adversarially-selected contexts. We adapt the information-theoretic perspective of \cite{RvR16} to the contextual setting by considering a lifted version of the information ratio defined in terms of the unknown model parameter instead of the optimal action or optimal policy as done in previous works on the same setting. This allows us to bound the regret in terms of the entropy of the prior distribution through a remarkably simple proof, and with no structural assumptions on the likelihood or the prior. The extension to priors with infinite entropy only requires a Lipschitz assumption on the log-likelihood. An interesting special case is that of logistic bandits with $d$-dimensional parameters, $K$ actions, and Lipschitz logits, for which we provide a $\widetilde{O}(\sqrt{dKT})$ regret upper-bound that does not depend on the smallest slope of the sigmoid link function.

Energy-based models parameterize the unnormalized log-probability of data samples, but there is a lack of guidance on how to construct the "energy". In this paper, we propose a Denoising-EBM which decomposes the image energy into "semantic energy" and "texture energy". We define the "semantic energy" in the latent space of DAE to model the high-level representations, and define the pixel-level reconstruction error for denoising as "texture energy". Inspired by score-based model, our model utilizes multi-scale noisy samples for maximum-likelihood training and it outputs a vector instead of a scalar for exploring a larger set of functions during optimization. After training, the semantics are first synthesized by fast MCMC through "semantic energy", and then the pixel-level refinement of semantic image will be performed to generate perfect samples based on "texture energy". Ultimately, our model can outperform most EBMs in image generation. And we also demonstrate that Denoising-EBM has top performance among EBMs for out-of-distribution detection.