NeurIPS 2023 论文列表

In this paper we offer a new perspective on the well established agglomerative clustering algorithm, focusing on recovery of hierarchical structure. We recommend a simple variant of the standard algorithm, in which clusters are merged by maximum average dot product and not, for example, by minimum distance or within-cluster variance. We demonstrate that the tree output by this algorithm provides a bona fide estimate of generative hierarchical structure in data, under a generic probabilistic graphical model. The key technical innovations are to understand how hierarchical information in this model translates into tree geometry which can be recovered from data, and to characterise the benefits of simultaneously growing sample size and data dimension. We demonstrate superior tree recovery performance with real data over existing approaches such as UPGMA, Ward's method, and HDBSCAN.

Langevin Monte Carlo (LMC) and its stochastic gradient versions are powerful algorithms for sampling from complex high-dimensional distributions. To sample from a distribution with density $\pi(\theta)\propto \exp(-U(\theta)) $, LMC iteratively generates the next sample by taking a step in the gradient direction $\nabla U$ with added Gaussian perturbations. Expectations w.r.t. the target distribution $\pi$ are estimated by averaging over LMC samples. In ordinary Monte Carlo, it is well known that the estimation error can be substantially reduced by replacing independent random samples by quasi-random samples like low-discrepancy sequences. In this work, we show that the estimation error of LMC can also be reduced by using quasi-random samples. Specifically, we propose to use completely uniformly distributed (CUD) sequences with certain low-discrepancy property to generate the Gaussian perturbations. Under smoothness and convexity conditions, we prove that LMC with a low-discrepancy CUD sequence achieves smaller error than standard LMC. The theoretical analysis is supported by compelling numerical experiments, which demonstrate the effectiveness of our approach.

Monte Carlo Tree Search (MCTS) algorithms such as AlphaGo and MuZero have achieved superhuman performance in many challenging tasks. However, the computational complexity of MCTS-based algorithms is influenced by the size of the search space. To address this issue, we propose a novel probability tree state abstraction (PTSA) algorithm to improve the search efficiency of MCTS. A general tree state abstraction with path transitivity is defined. In addition, the probability tree state abstraction is proposed for fewer mistakes during the aggregation step. Furthermore, the theoretical guarantees of the transitivity and aggregation error bound are justified. To evaluate the effectiveness of the PTSA algorithm, we integrate it with state-of-the-art MCTS-based algorithms, such as Sampled MuZero and Gumbel MuZero. Experimental results on different tasks demonstrate that our method can accelerate the training process of state-of-the-art algorithms with 10%-45% search space reduction.