Recent research has developed several Monte Carlo methods for estimating the normalization constant (partition function) based on the idea of annealing. This means sampling successively from a path of distributions that interpolate between a tractable "proposal" distribution and the unnormalized "target" distribution. Prominent estimators in this family include annealed importance sampling and annealed noise-contrastive estimation (NCE). Such methods hinge on a number of design choices: which estimator to use, which path of distributions to use and whether to use a path at all; so far, there is no definitive theory on which choices are efficient. Here, we evaluate each design choice by the asymptotic estimation error it produces.

Discharge summaries in Electronic Health Records (EHRs) are crucial for clinical decision-making, but their length and complexity make information extraction challenging, especially when dealing with accumulated summaries across multiple patient admissions.

This paper introduces a novel approach using Large Language Models (LLMs) integrated into an agent framework for flexible and effective personal mobility generation. LLMs overcome the limitations of previous models by effectively processing semantic data and offering versatility in modeling various tasks.

In multiplayer games, self-interested behavior among the players can harm the social welfare. Tax mechanisms are a common method to alleviate this issue and induce socially optimal behavior. In this work, we take the initial step of learning the optimal tax that can maximize social welfare with limited feedback in congestion games. We propose a new type of feedback named equilibrium feedback, where the tax designer can only observe the Nash equilibrium after deploying a tax plan. Existing algorithms are not applicable due to the exponentially large tax function space, nonexistence of the gradient, and nonconvexity of the objective. To tackle these challenges, we design a computationally efficient algorithm that leverages several novel components: (1) a piece-wise linear tax to approximate the optimal tax; (2) extra linear terms to guarantee a strongly convex potential function; (3) an efficient subroutine to find the exploratory tax that can provide critical information about the game.

We evaluate TPSR and several baseline methods on the following four standard benchmark datasets: Feynman, Black-box, and Strogatz from SRBench [42], and In-domain Synthetic Data generated based on [18]. More details on each of these datasets are given below. The regression input points (x, y) from these equations are provided in Penn Machine Learning Benchmark (PMLB) [42, 43] and have been studied in SRBench [42] for the symbolic regression task. The input dimension is limited to d 10 and the true underlying function of points is known. We split the dataset into B bags of 200 input points (when N is larger than 200) since the transformer SR model is pretrained on N 200 input points as per [18]. The input points for these problems are included in PMLB [43] and have been examined in SRBench [42] for symbolic regression. The input dimension for these problems is restricted to d = 2 and the true underlying functions are provided. The aim of SR study on these black-box datasets is to find an interpretable model expression that fits the data effectively.

Symbolic regression (SR) is a challenging task in machine learning that involves finding a mathematical expression for a function based on its values. Recent advancements in SR have demonstrated the effectiveness of pre-trained transformer models in generating equations as sequences, leveraging large-scale pre-training on synthetic datasets and offering notable advantages in terms of inference time over classical Genetic Programming (GP) methods. However, these models primarily rely on supervised pre-training objectives borrowed from text generation and overlook equation discovery goals like accuracy and complexity. To address this, we propose TPSR, a Transformer-based Planning strategy for Symbolic Regression that incorporates Monte Carlo Tree Search planning algorithm into the transformer decoding process. Unlike conventional decoding strategies, TPSR enables the integration of non-differentiable equation verification feedback, such as fitting accuracy and complexity, as external sources of knowledge into the transformer equation generation process. Extensive experiments on various datasets show that our approach outperforms state-of-the-art methods, enhancing the model's fitting-complexity trade-off, extrapolation abilities, and robustness to noise

Owing to advancements in image synthesis techniques, stylization methodologies for large models have garnered remarkable outcomes. However, when it comes to processing facial images, the outcomes frequently fall short of expectations. Facial stylization is predominantly challenged by two significant hurdles. Firstly, obtaining a large dataset of high-quality stylized images is difficult. The scarcity and diversity of artistic styles make it impractical to compile comprehensive datasets for each style.