Discrete-time diffusion-based generative models and score matching methods have shown promising results in modeling high-dimensional image data. Recently, Song et al. (2021) show that diffusion processes that transform data into noise can be reversed via learning the score function, i.e. the gradient of the logdensity of the perturbed data. They propose to plug the learned score function into an inverse formula to define a generative diffusion process. Despite the empirical success, a theoretical underpinning of this procedure is still lacking. In this work, we approach the (continuous-time) generative diffusion directly and derive a variational framework for likelihood estimation, which includes continuous-time normalizing flows as a special case, and can be seen as an infinitely deep variational autoencoder. Under this framework, we show that minimizing the score-matching loss is equivalent to maximizing a lower bound of the likelihood of the plug-in reverse SDE proposed by Song et al. (2021), bridging the theoretical gap.

Mixed-integer linear programming (MILP) is one of the most popular mathematical formulations with numerous applications. In practice, improving the performance of MILP solvers often requires a large amount of high-quality data, which can be challenging to collect. Researchers thus turn to generation techniques to generate additional MILP instances. However, existing approaches do not take into account specific block structures--which are closely related to the problem formulations-- in the constraint coefficient matrices (CCMs) of MILPs. Consequently, they are prone to generate computationally trivial or infeasible instances due to the disruptions of block structures and thus problem formulations.

We study distributed learning of nonparametric conditional quantiles with Tikhonov regularization in a reproducing kernel Hilbert space (RKHS). Although distributed parametric quantile regression has been investigated in several existing works, the current nonparametric quantile setting poses different challenges and is still unexplored. The difficulty lies in the illusive explicit bias-variance decomposition in the quantile RKHS setting as in the regularized least squares regression. For the simple divide-and-conquer approach that partitions the data set into multiple parts and then takes an arithmetic average of the individual outputs, we establish the risk bounds using a novel second-order empirical process for quantile risk.

The ability of a document classifier to handle inputs that are drawn from a distribution different from the training distribution is crucial for robust deployment and generalizability. The RVL-CDIP corpus [18] is the de facto standard benchmark for document classification, yet to our knowledge all studies that use this corpus do not include evaluation on out-of-distribution documents. In this paper, we curate and release a new out-of-distribution benchmark for evaluating out-of-distribution performance for document classifiers. Our new out-of-distribution benchmark consists of two types of documents: those that are not part of any of the 16 indomain RVL-CDIP categories (RVL-CDIP-O), and those that are one of the 16 in-domain categories yet are drawn from a distribution different from that of the original RVL-CDIP dataset (RVL-CDIP-N). While prior work on document classification for in-domain RVL-CDIP documents reports high accuracy scores, we find that these models exhibit accuracy drops of between roughly 15-30% on our new out-of-domain RVL-CDIP-N benchmark, and further struggle to distinguish between in-domain RVL-CDIP-N and out-of-domain RVL-CDIP-O inputs. Our new benchmark provides researchers with a valuable new resource for analyzing out-ofdistribution performance on document classifiers.

In environments with delayed observation, state augmentation by including actions within the delay window is adopted to retrieve Markovian property to enable reinforcement learning (RL). However, state-of-the-art (SOTA) RL techniques with Temporal-Difference (TD) learning frameworks often suffer from learning inefficiency, due to the significant expansion of the augmented state space with the delay. To improve learning efficiency without sacrificing performance, this work introduces a novel framework called Variational Delayed Policy Optimization (VDPO), which reformulates delayed RL as a variational inference problem. This problem is further modelled as a two-step iterative optimization problem, where the first step is TD learning in the delay-free environment with a small state space, and the second step is behaviour cloning which can be addressed much more efficiently than TD learning. We not only provide a theoretical analysis of VDPO in terms of sample complexity and performance, but also empirically demonstrate that VDPO can achieve consistent performance with SOTA methods, with a significant enhancement of sample efficiency (approximately 50% less amount of samples) in the MuJoCo benchmark.

For preparation, we first introduce an importance sampling framework for coreset construction, called the Feldman-Langberg framework [27, 13]. A.1 The Feldman-Langberg framework We first give the definition of query space and the corresponding coresets. The tuple (X, u, P, f) is called a query space. Specifically, if u(x) = 1 for all x X, we use (X, P, f) for simplicity. Intuitively, f represents a linear combination of weighted functions indexed by X, and P represents the ground set of f.

We study the problem of constructing coresets for clustering problems with time series data. This problem has gained importance across many fields including biology, medicine, and economics due to the proliferation of sensors for real-time measurement and rapid drop in storage costs.