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).

We examine whether large neural language models, trained on very large collections of varied English text, learn the potentially long-distance dependency of British versus American spelling conventions, i.e., whether spelling is consistently one or the other within model-generated strings. In contrast to long-distance dependencies in non-surface underlying structure (e.g., syntax), spelling consistency is easier to measure both in LMs and the text corpora used to train them, which can provide additional insight into certain observed model behaviors. Using a set of probe words unique to either British or American English, we first establish that training corpora exhibit substantial (though not total) consistency. A large T5 language model does appear to internalize this consistency, though only with respect to observed lexical items (not nonce words with British/American spelling patterns). We further experiment with correcting for biases in the training data by fine-tuning T5 on synthetic data that has been debiased, and find that finetuned T5 remains only somewhat sensitive to spelling consistency. Further experiments show GPT2 to be similarly limited.

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.

In recent years, Reinforcement Learning (RL) has been applied to real-world problems with increasing success. Such applications often require to put constraints on the agent's behavior. Existing algorithms for constrained RL (CRL) rely on gradient descent-ascent, but this approach comes with a caveat. While these algorithms are guaranteed to converge on average, they do not guarantee last-iterate convergence, i.e., the current policy of the agent may never converge to the optimal solution. In practice, it is often observed that the policy alternates between satisfying the constraints and maximizing the reward, rarely accomplishing both objectives simultaneously. Here, we address this problem by introducing Reinforcement Learning with Optimistic Ascent-Descent (ReLOAD), a principled CRL method with guaranteed last-iterate convergence. We demonstrate its empirical effectiveness on a wide variety of CRL problems including discrete MDPs and continuous control. In the process we establish a benchmark of challenging CRL problems.

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.

Quantum Bayesian Computation (QBC) is an emerging field that levers the computational gains available from quantum computers to provide an exponential speed-up in Bayesian computation. Our paper adds to the literature in two ways. First, we show how von Neumann quantum measurement can be used to simulate machine learning algorithms such as Markov chain Monte Carlo (MCMC) and Deep Learning (DL) that are fundamental to Bayesian learning. Second, we describe data encoding methods needed to implement quantum machine learning including the counterparts to traditional feature extraction and kernel embeddings methods. Our goal then is to show how to apply quantum algorithms directly to statistical machine learning problems. On the theoretical side, we provide quantum versions of high dimensional regression, Gaussian processes (Q-GP) and stochastic gradient descent (Q-SGD). On the empirical side, we apply a Quantum FFT model to Chicago housing data. Finally, we conclude with directions for future research.

We propose a method for optimal Bayesian filtering with deterministic particles. In order to avoid particle degeneration, the filter step is not performed at once. Instead, the particles progressively flow from prior to posterior. This is achieved by splitting the filter step into a series of sub-steps. In each sub-step, optimal resampling is done by a map that replaces non-equally weighted particles with equally weighted ones. Inversions of the maps or monotonicity constraints are not required, greatly simplifying the procedure. The parameters of the mapping network are optimized w.r.t.\ to a particle set distance. This distance is differentiable, and compares non-equally and equally weighted particles. Composition of the map sequence provides a final mapping from prior to posterior particles. Radial basis function neural networks are used as maps. It is important that no intermediate continuous density representation is required. The entire flow works directly with particle representations. This avoids costly density estimation.