Meta-learning aims to extract useful inductive biases from a set of related datasets. In Bayesian meta-learning, this is typically achieved by constructing a prior distribution over neural network parameters. However, specifying families of computationally viable prior distributions over the high-dimensional neural network parameters is difficult. As a result, existing approaches resort to meta-learning restrictive diagonal Gaussian priors, severely limiting their expressiveness and performance. To circumvent these issues, we approach meta-learning through the lens of functional Bayesian neural network inference, which views the prior as a stochastic process and performs inference in the function space. Specifically, we view the meta-training tasks as samples from the data-generating process and formalize meta-learning as empirically estimating the law of this stochastic process. Our approach can seamlessly acquire and represent complex prior knowledge by meta-learning the score function of the data-generating process marginals instead of parameter space priors. In a comprehensive benchmark, we demonstrate that our method achieves state-of-the-art performance in terms of predictive accuracy and substantial improvements in the quality of uncertainty estimates.

Spanning tree problems with specialized constraints can be difficult to solve in real-world scenarios, often requiring intricate algorithmic design and exponential time. Recently, there has been growing interest in end-to-end deep neural networks for solving routing problems. However, such methods typically produce sequences of vertices, which makes it difficult to apply them to general combinatorial optimization problems where the solution set consists of edges, as in various spanning tree problems. In this paper, we propose NeuroPrim, a novel framework for solving various spanning tree problems by defining a Markov Decision Process (MDP) for general combinatorial optimization problems on graphs. Our approach reduces the action and state space using Prim's algorithm and trains the resulting model using REINFORCE. We apply our framework to three difficult problems on Euclidean space: the Degree-constrained Minimum Spanning Tree (DCMST) problem, the Minimum Routing Cost Spanning Tree (MRCST) problem, and the Steiner Tree Problem in graphs (STP). Experimental results on literature instances demonstrate that our model outperforms strong heuristics and achieves small optimality gaps of up to 250 vertices. Additionally, we find that our model has strong generalization ability, with no significant degradation observed on problem instances as large as 1000. Our results suggest that our framework can be effective for solving a wide range of combinatorial optimization problems beyond spanning tree problems.

We consider the problem of solving robust Markov decision process (MDP), which involves a set of discounted, finite state, finite action space MDPs with uncertain transition kernels. The goal of planning is to find a robust policy that optimizes the worst-case values against the transition uncertainties, and thus encompasses the standard MDP planning as a special case. For $(\mathbf{s},\mathbf{a})$-rectangular uncertainty sets, we establish several structural observations on the robust objective, which facilitates the development of a policy-based first-order method, namely the robust policy mirror descent (RPMD). An $\mathcal{O}(\log(1/\epsilon))$ iteration complexity for finding an $\epsilon$-optimal policy is established with linearly increasing stepsizes. We further develop a stochastic variant of the robust policy mirror descent method, named SRPMD, when the first-order information is only available through online interactions with the nominal environment. We show that the optimality gap converges linearly up to the noise level, and consequently establish an $\tilde{\mathcal{O}}(1/\epsilon^2)$ sample complexity by developing a temporal difference learning method for policy evaluation. Both iteration and sample complexities are also discussed for RPMD with a constant stepsize. To the best of our knowledge, all the aforementioned results appear to be new for policy-based first-order methods applied to the robust MDP problem.

This paper investigates conservative exploration in reinforcement learning where the performance of the learning agent is guaranteed to be above a certain threshold throughout the learning process. It focuses on the tabular episodic Markov Decision Process (MDP) setting that has finite states and actions. With the knowledge of an existing safe baseline policy, an algorithm termed as StepMix is proposed to balance the exploitation and exploration while ensuring that the conservative constraint is never violated in each episode with high probability. StepMix features a unique design of a mixture policy that adaptively and smoothly interpolates between the baseline policy and the optimistic policy. Theoretical analysis shows that StepMix achieves near-optimal regret order as in the constraint-free setting, indicating that obeying the stringent episode-wise conservative constraint does not compromise the learning performance. Besides, a randomization-based EpsMix algorithm is also proposed and shown to achieve the same performance as StepMix. The algorithm design and theoretical analysis are further extended to the setting where the baseline policy is not given a priori but must be learned from an offline dataset, and it is proved that similar conservative guarantee and regret can be achieved if the offline dataset is sufficiently large. Experiment results corroborate the theoretical analysis and demonstrate the effectiveness of the proposed conservative exploration strategies.

It has become common to perform kinetic analysis using approximate Koopman operators that transforms high-dimensional time series of observables into ranked dynamical modes. Key to a practical success of the approach is the identification of a set of observables which form a good basis in which to expand the slow relaxation modes. Good observables are, however, difficult to identify {\em a priori} and sub-optimal choices can lead to significant underestimations of characteristic timescales. Leveraging the representation of slow dynamics in terms of Hidden Markov Model (HMM), we propose a simple and computationally efficient clustering procedure to infer surrogate observables that form a good basis for slow modes. We apply the approach to an analytically solvable model system, as well as on three protein systems of different complexities. We consistently demonstrate that the inferred indicator functions can significantly improve the estimation of the leading eigenvalues of the Koopman operators and correctly identify key states and transition timescales of stochastic systems, even when good observables are not known {\em a priori}.

Datasets in the real world are often complex and to some degree hierarchical, with groups and sub-groups of data sharing common characteristics at different levels of abstraction. Understanding and uncovering the hidden structure of these datasets is an important task that has many practical applications. To address this challenge, we present a new and general method for building relational data trees by exploiting the learning dynamics of the Restricted Boltzmann Machine (RBM). Our method is based on the mean-field approach, derived from the Plefka expansion, and developed in the context of disordered systems. It is designed to be easily interpretable. We tested our method in an artificially created hierarchical dataset and on three different real-world datasets (images of digits, mutations in the human genome, and a homologous family of proteins). The method is able to automatically identify the hierarchical structure of the data. This could be useful in the study of homologous protein sequences, where the relationships between proteins are critical for understanding their function and evolution.

The past three decades have witnessed notable success in designing efficient SAT solvers, with modern solvers capable of solving industrial benchmarks containing millions of variables in just a few seconds. The success of modern SAT solvers owes to the widely-used CDCL algorithm, which lacks comprehensive theoretical investigation. Furthermore, it has been observed that CDCL solvers still struggle to deal with specific classes of benchmarks comprising only hundreds of variables, which contrasts with their widespread use in real-world applications. Consequently, there is an urgent need to uncover the inner workings of these seemingly weak yet powerful black boxes. In this paper, we present a first step towards this goal by introducing an approach called CausalSAT, which employs causal reasoning to gain insights into the functioning of modern SAT solvers. CausalSAT initially generates observational data from the execution of SAT solvers and learns a structured graph representing the causal relationships between the components of a SAT solver. Subsequently, given a query such as whether a clause with low literals blocks distance (LBD) has a higher clause utility, CausalSAT calculates the causal effect of LBD on clause utility and provides an answer to the question. We use CausalSAT to quantitatively verify hypotheses previously regarded as "rules of thumb" or empirical findings such as the query above. Moreover, CausalSAT can address previously unexplored questions, like which branching heuristic leads to greater clause utility in order to study the relationship between branching and clause management. Experimental evaluations using practical benchmarks demonstrate that CausalSAT effectively fits the data, verifies four "rules of thumb", and provides answers to three questions closely related to implementing modern solvers.

We introduce the concept of programmable feature Our key motivation comes from a novel dynamical Ising-like engineering for time series modeling and propose model, the spin-gas Glauber dynamics, originated from a a feature programming framework. This newly debuted gas-like interaction that includes momentum framework generates large amounts of predictive and acceleration information. By using spin-gas Glauber features for noisy multivariate time series while dynamics as the fundamental model for time series generating allowing users to incorporate their inductive bias processes at the smallest time scale, we explore the with minimal effort. The key motivation of our potential of treating time series as the path-sum of infinitesimal framework is to view any multivariate time series increments generated by a series of Markovian coin as a cumulative sum of fine-grained trajectory tosses following the spin-gas Glauber dynamics. From such increments, with each increment governed by a a fine-grained perspective, a set of operators is motivated for novel spin-gas dynamical Ising model.

Real-time demand prediction is a critical input for dynamic bus routing. While many researchers have developed numerous complex methods to predict short-term transit demand, the applications have been limited to short, stable time frames and a few stations. How these methods perform in highly dynamic environments has not been studied, nor has their performance been systematically compared. We built an open-source infrastructure with five common methodologies, including econometric and deep learning approaches, and assessed their performance under stable and highly dynamic conditions. We used a time series from smartcard data to predict demand for the following day for the BRT system in Bogota, Colombia. The dynamic conditions in the time series include a month-long protest and the COVID-19 pandemic. Both conditions triggered drastic shifts in demand. The results reveal that most tested models perform similarly in stable conditions, with MAAPE varying from 0.08 to 0.12. The benchmark demonstrated that all models performed significantly worse in both dynamic conditions compared to the stable conditions. In the month-long protest, the increased MAAPE ranged from 0.14 to 0.24. Similarly, during the COVID-19 pandemic, the increased MAAPE ranged from 0.12 to 0.82. Notably, in the COVID-19 pandemic condition, an LSTM model with adaptive training and a multi-output design outperformed other models, adapting faster to disruptions. The prediction error stabilized within approximately 1.5 months, whereas other models continued to exhibit higher error rates even a year after the start of the pandemic. The aim of this open-source codebase infrastructure is to lower the barrier for other researchers to replicate and reproduce models, facilitate a collective effort within the research community to improve the benchmarking process and accelerate the advancement of short-term ridership prediction models.

This study aims to investigate the utilization of Bayesian techniques for the calibration of micro-electro-mechanical systems (MEMS) accelerometers. These devices have garnered substantial interest in various practical applications and typically require calibration through error-correcting functions. The parameters of these error-correcting functions are determined during a calibration process. However, due to various sources of noise, these parameters cannot be determined with precision, making it desirable to incorporate uncertainty in the calibration models. Bayesian modeling offers a natural and complete way of reflecting uncertainty by treating the model parameters as variables rather than fixed values. Additionally, Bayesian modeling enables the incorporation of prior knowledge, making it an ideal choice for calibration. Nevertheless, it is infrequently used in sensor calibration. This study introduces Bayesian methods for the calibration of MEMS accelerometer data in a straightforward manner using recent advances in probabilistic programming.