Approximate nearest neighbor (ANN) search is a fundamental algorithmic problem.

Predictive models make mistakes. Hence, there is a need to quantify the uncertainty associated with their predictions. Conformal inference has emerged as a powerful tool to create statistically valid prediction regions around point predictions, but its naive application to regression problems yields non-adaptive regions. New conformal scores, often relying upon quantile regressors or conditional density estimators, aim to address this limitation. Although they are useful for creating prediction bands, these scores are detached from the original goal of quantifying the uncertainty around an arbitrary predictive model. This paper presents a new, model-agnostic family of methods to calibrate prediction intervals for regression problems with local coverage guarantees. Our approach is based on pursuing the coarsest partition of the feature space that approximates conditional coverage. We create this partition by training regression trees and Random Forests on conformity scores. Our proposal is versatile, as it applies to various conformity scores and prediction settings and demonstrates superior scalability and performance compared to established baselines in simulated and real-world datasets. We provide a Python package locart that implements our methods using the standard scikit-learn interface.

Approximating integrals with respect to a complicated, highdimensional probability distribution π is an important problem spanning multiple disciplines, such as Bayesian statistical inference, machine learning, statistical physics, and theoretical computer science [13, 17]. Sequential Monte Carlo (SMC) methods are a large class of stochastic approximation algorithms designed to solve these problems by combining Markov chain Monte Carlo (MCMC) methods and resampling strategies to sequentially sample from a series of probability distributions. Some examples of SMC algorithms include population Monte Carlo methods [2], annealed importance sampling [27], sequential particle filters [3], and population annealing [40], among many others [15]. Closely related - but purely MCMC - methods include parallel tempering (PT) [14] and simulated tempering (ST) [23], which have been referred to as population-based MCMC methods [15]. An SMC sampler is generally constructed as follows.

We consider the Lipschitz bandit optimization problem with an emphasis on practical efficiency. Although there is rich literature on regret analysis of this type of problem, e.g., [Kleinberg et al. 2008, Bubeck et al. 2011, Slivkins 2014], their proposed algorithms suffer from serious practical problems including extreme time complexity and dependence on oracle implementations. With this motivation, we propose a novel algorithm with an Upper Confidence Bound (UCB) exploration, namely Tree UCB-Hoeffding, using adaptive partitions. Our partitioning scheme is easy to implement and does not require any oracle settings. With a tree-based search strategy, the total computational cost can be improved to $\mathcal{O}(T\log T)$ for the first $T$ iterations. In addition, our algorithm achieves the regret lower bound up to a logarithmic factor.

This paper presents a novel SHOI tableau calculus which incorporates algebraic reasoning for deciding ontology consistency. Numerical restrictions imposed by nominals, existential and universal restrictions are encoded into a set of linear inequalities. Column generation and branch-and-price algorithms are used to solve these inequalities. Our preliminary experiments indicate that this calculus performs better on SHOI ontologies than standard tableau methods.

Editor: Bayesian networks are probabilistic graphical models widely employed to understand dependencies in high dimensional data, and even to facilitate causal discovery. Learning the underlying network structure, which is encoded as a directed acyclic graph (DAG) is highly challenging mainly due to the vast number of possible networks. Efforts have focussed on two fronts: constraint based methods that perform conditional independence tests to exclude edges and score and search approaches which explore the DAG space with greedy or MCMC schemes. Here we synthesise these two fields in a novel hybrid method which reduces the complexity of MCMC approaches to that of a constraint based method. Individual steps in the MCMC scheme only require simple table lookups so that very long chains can be efficiently obtained. Furthermore, the scheme includes an iterative procedure to correct for errors from the conditional independence tests. The algorithm not only offers markedly superior performance to alternatives, but DAGs can also be sampled from the posterior distribution enabling full Bayesian modelling averaging for much larger Bayesian networks.

We propose an efficient algorithm for approximate computation of the profile maximum likelihood (PML), a variant of maximum likelihood maximizing the probability of observing a sufficient statistic rather than the empirical sample. The PML has appealing theoretical properties, but is difficult to compute exactly. Inspired by observations gleaned from exactly solvable cases, we look for an approximate PML solution, which, intuitively, clumps comparably frequent symbols into one symbol. This amounts to lower-bounding a certain matrix permanent by summing over a subgroup of the symmetric group rather than the whole group during the computation. We extensively experiment with the approximate solution, and find the empirical performance of our approach is competitive and sometimes significantly better than state-of-the-art performance for various estimation problems.