In sampling-based Bayesian models of brain function, neural activities are assumed to be samples from probability distributions that the brain uses for probabilistic computation. However, a comprehensive understanding of how mechanistic models of neural dynamics can sample from arbitrary distributions is still lacking. We use tools from functional analysis and stochastic differential equations to explore the minimum architectural requirements for $\textit{recurrent}$ neural circuits to sample from complex distributions. We first consider the traditional sampling model consisting of a network of neurons whose outputs directly represent the samples (sampler-only network). We argue that synaptic current and firing-rate dynamics in the traditional model have limited capacity to sample from a complex probability distribution. We show that the firing rate dynamics of a recurrent neural circuit with a separate set of output units can sample from an arbitrary probability distribution. We call such circuits reservoir-sampler networks (RSNs). We propose an efficient training procedure based on denoising score matching that finds recurrent and output weights such that the RSN implements Langevin sampling. We empirically demonstrate our model's ability to sample from several complex data distributions using the proposed neural dynamics and discuss its applicability to developing the next generation of sampling-based brain models.

We investigate the problem of corruption robustness in offline reinforcement learning (RL) with general function approximation, where an adversary can corrupt each sample in the offline dataset, and the corruption level $\zeta\geq0$ quantifies the cumulative corruption amount over $n$ episodes and $H$ steps. Our goal is to find a policy that is robust to such corruption and minimizes the suboptimality gap with respect to the optimal policy for the uncorrupted Markov decision processes (MDPs). Drawing inspiration from the uncertainty-weighting technique from the robust online RL setting \citep{he2022nearly,ye2022corruptionrobust}, we design a new uncertainty weight iteration procedure to efficiently compute on batched samples and propose a corruption-robust algorithm for offline RL. Notably, under the assumption of single policy coverage and the knowledge of $\zeta$, our proposed algorithm achieves a suboptimality bound that is worsened by an additive factor of $\mathcal O(\zeta \cdot (\text{CC}(\lambda,\hat{\mathcal F},\mathcal Z_n^H))^{1/2} (C(\hat{\mathcal F},\mu))^{-1/2} n^{-1})$ due to the corruption. Here $\text{CC}(\lambda,\hat{\mathcal F},\mathcal Z_n^H)$ is the coverage coefficient that depends on the regularization parameter $\lambda$, the confidence set $\hat{\mathcal F}$, and the dataset $\mathcal Z_n^H$, and $C(\hat{\mathcal F},\mu)$ is a coefficient that depends on $\hat{\mathcal F}$ and the underlying data distribution $\mu$. When specialized to linear MDPs, the corruption-dependent error term reduces to $\mathcal O(\zeta d n^{-1})$ with $d$ being the dimension of the feature map, which matches the existing lower bound for corrupted linear MDPs. This suggests that our analysis is tight in terms of the corruption-dependent term.

Phase transitions, characterized by abrupt shifts between macroscopic patterns of organization, are ubiquitous in complex systems. Despite considerable research in the physical and natural sciences, the empirical study of this phenomenon in societal systems is relatively underdeveloped. The goal of this study is to explore whether the dynamics of collective civil unrest can be plausibly characterized as a sequence of recurrent phase shifts, with each phase having measurable and identifiable latent characteristics. Building on previous efforts to characterize civil unrest as a self-organized critical system, we introduce a macro-level statistical model of civil unrest and evaluate its plausibility using a comprehensive dataset of civil unrest events in 170 countries from 1946 to 2017. Our findings demonstrate that the macro-level phase model effectively captures the characteristics of civil unrest data from diverse countries globally and that universal mechanisms may underlie certain aspects of the dynamics of civil unrest. We also introduce a scale to quantify a country's long-term unrest per unit of time and show that civil unrest events tend to cluster geographically, with the magnitude of civil unrest concentrated in specific regions. Our approach has the potential to identify and measure phase transitions in various collective human phenomena beyond civil unrest, contributing to a better understanding of complex social systems.

Such assessments are Response Theory (IRT) to capture temporal dynamics in referred to as formative assessments and are used not only learner ability. While these models have the potential to allow to track student learning and make appropriate instructional instructional systems to actively monitor the evolution interventions, but also to allow learners to practice their of learner proficiency in real time, existing dynamic item response knowledge and skills, and make necessary self-corrections models rely on expensive inference algorithms that [17]. When learning occurs alongside assessment, learner scale poorly to massive datasets. In this work, we propose proficiency is longitudinal rather than inert, and the assumption Variational Temporal IRT (VTIRT) for fast and accurate of static proficiency makes standard IRT less suitable inference of dynamic learner proficiency. VTIRT offers orders as a model of proficiency measurement. of magnitude speedup in inference runtime while still providing accurate inference. Moreover, the proposed algorithm Dynamic Item Response models [14, 11] mitigate this issue is intrinsically interpretable by virtue of its modular by removing the assumptions of static ability and instead allowing design. When applied to 9 real student datasets, VTIRT it to stochastically change over time, but existing inference consistently yields improvements in predicting future learner methods rely on expensive iterative algorithms with performance over other learner proficiency models.

Applying a machine learning model for decision-making in the real world requires to distinguish what the model knows from what it does not. A critical factor in assessing the knowledge of a model is to quantify its predictive uncertainty. Predictive uncertainty is commonly measured by the entropy of the Bayesian model average (BMA) predictive distribution. Yet, the properness of this current measure of predictive uncertainty was recently questioned. We provide new insights regarding those limitations. Our analyses show that the current measure erroneously assumes that the BMA predictive distribution is equivalent to the predictive distribution of the true model that generated the dataset. Consequently, we introduce a theoretically grounded measure to overcome these limitations. We experimentally verify the benefits of our introduced measure of predictive uncertainty. We find that our introduced measure behaves more reasonably in controlled synthetic tasks. Moreover, our evaluations on ImageNet demonstrate that our introduced measure is advantageous in real-world applications utilizing predictive uncertainty.

We establish Frequentist properties, i.e., posterior consistency, asymptotic normality, and posterior contraction rates, for the distributed (non-)Bayes Inference problem for a set of agents connected over a network. These results are motivated by the need to analyze large, decentralized datasets, where distributed (non)-Bayesian inference has become a critical research area across multiple fields, including statistics, machine learning, and economics. Our results show that, under appropriate assumptions on the communication graph, distributed (non)-Bayesian inference retains parametric efficiency while enhancing robustness in uncertainty quantification. We also explore the trade-off between statistical efficiency and communication efficiency by examining how the design and size of the communication graph impact the posterior contraction rate. Furthermore, we extend our analysis to time-varying graphs and apply our results to exponential family models, distributed logistic regression, and decentralized detection models.

Over the last decades, the family of $\alpha$-stale distributions has proven to be useful for modelling in telecommunication systems. Particularly, in the case of radar applications, finding a fast and accurate estimation for the amplitude density function parameters appears to be very important. In this work, the maximum likelihood estimator (MLE) is proposed for parameters of the amplitude distribution. To do this, the amplitude data are \emph{projected} on the horizontal and vertical axes using two simple transformations. It is proved that the \emph{projected} data follow a zero-location symmetric $\alpha$-stale distribution for which the MLE can be computed quite fast. The average of computed MLEs based on two \emph{projections} is considered as estimator for parameters of the amplitude distribution. Performance of the proposed \emph{projection} method is demonstrated through simulation study and analysis of two sets of real radar data.

It has become common sense that transferring intrinsic information from teachers to the greatest extent can expedite a student's learning progress, especially in machine learning given versatile and powerful teacher models. Learning with their assistance has been coined knowledge distillation (KD) (Hinton et al., 2015; Lopez-Paz et al., 2015), a famous paradigm of knowledge transfer leading to remarkable empirical effectiveness in classification tasks across various downstream applications (Gou et al., 2021; Wang and Yoon, 2021; Gu et al., 2023b). The term distillation implies a belief that the inscrutable teacher(s) may possess useful yet complicated structural information, which we should be able to compress and inject into a compact one, i.e., the student model (Breiman and Shang, 1996; Buciluǎ et al., 2006; Li et al., 2014; Ba and Caruana, 2014; Allen-Zhu and Li, 2020). This has guided the community towards a line of knowledge transfer methods featuring the awareness of teacher training details or snapshots, such as the original training set, the intermediate activations, the last-layer logits (for a probabilistic classifier), the first-or second-order derivative or statistical information, and even task-specific knowledge (Hinton et al., 2015; Furlanello et al., 2018; Cho and Hariharan, 2019; Zhao et al., 2022; Romero et al., 2014; Zagoruyko and Komodakis, 2016;

Artificial intelligence experienced a technological breakthrough in science, industry, and everyday life in the recent few decades. The advancements can be credited to the ever-increasing availability and miniaturization of computational resources that resulted in exponential data growth. However, because of the insufficient amount of data in some cases, employing machine learning in solving complex tasks is not straightforward or even possible. As a result, machine learning with small data experiences rising importance in data science and application in several fields. The authors focus on interpreting the general term of "small data" and their engineering and industrial application role. They give a brief overview of the most important industrial applications of machine learning and small data. Small data is defined in terms of various characteristics compared to big data, and a machine learning formalism was introduced. Five critical challenges of machine learning with small data in industrial applications are presented: unlabeled data, imbalanced data, missing data, insufficient data, and rare events. Based on those definitions, an overview of the considerations in domain representation and data acquisition is given along with a taxonomy of machine learning approaches in the context of small data.

Causal discovery is becoming a key part in medical AI research. These methods can enhance healthcare by identifying causal links between biomarkers, demographics, treatments and outcomes. They can aid medical professionals in choosing more impactful treatments and strategies. In parallel, Large Language Models (LLMs) have shown great potential in identifying patterns and generating insights from text data. In this paper we investigate applying LLMs to the problem of determining the directionality of edges in causal discovery. Specifically, we test our approach on a deidentified set of Non Small Cell Lung Cancer(NSCLC) patients that have both electronic health record and genomic panel data. Graphs are validated using Bayesian Dirichlet estimators using tabular data. Our result shows that LLMs can accurately predict the directionality of edges in causal graphs, outperforming existing state-of-the-art methods. These findings suggests that LLMs can play a significant role in advancing causal discovery and help us better understand complex systems.