In this work, we consider the setting of heavy-tailed noise proposed by Zhang et al., (2020) [32],

The recently-proposed framework of Predict+Optimize tackles optimization problems with parameters that are unknown at solving time, in a supervised learning setting. Prior frameworks consider only the scenario where all unknown parameters are (eventually) revealed at the same time. In this work, we propose Multi-Stage Predict+Optimize, a novel extension catering to applications where unknown parameters are instead revealed in sequential stages, with optimization decisions made in between. We further develop three training algorithms for neural networks (NNs) for our framework as proof of concept, all of which can handle mixed integer linear programs. The first baseline algorithm is a natural extension of prior work, training a single NN which makes a single prediction of unknown parameters.

Neural Processes combine the strengths of neural networks and Gaussian processes to achieve both flexible learning and fast prediction in stochastic processes. However, a large class of problems comprises underlying temporal dependency structures in a sequence of stochastic processes that Neural Processes (NP) do not explicitly consider. In this paper, we propose Sequential Neural Processes (SNP) which incorporates a temporal state-transition model of stochastic processes and thus extends its modeling capabilities to dynamic stochastic processes. In applying SNP to dynamic 3D scene modeling, we introduce the Temporal Generative Query Networks. To our knowledge, this is the first 4D model that can deal with the temporal dynamics of 3D scenes. In experiments, we evaluate the proposed methods in dynamic (non-stationary) regression and 4D scene inference and rendering.

In this paper, we consider the problem of learning an unknown graph via queries on groups of nodes, with the result indicating whether or not at least one edge is present among those nodes.

The weights and the parameter k N regulate its bias-variance trade-off, and the trade-off implicitly affects the convergence rate of the excess risk for the k-NN classifier; several existing studies considered selecting optimal k and weights to obtain faster convergence rate. Whereas k-NN with non-negative weights has been developed widely, it was also proved that negative weights are essential for eradicating the bias terms and attaining optimal convergence rate. In this paper, we propose a novel multiscale k-NN (MS-k-NN), that extrapolates unweighted k-NN estimators from several k 1 values to k = 0, thus giving an imaginary 0-NN estimator. Our method implicitly computes optimal real-valued weights that are adaptive to the query and its neighbour points. We theoretically prove that the MS-k-NN attains the improved rate, which coincides with the existing optimal rate under some conditions.

This study presents a physics-informed machine learning-based control method for nonlinear dynamic systems with highly noisy measurements. Existing data-driven control methods that use machine learning for system identification cannot effectively cope with highly noisy measurements, resulting in unstable control performance. To address this challenge, the present study extends current physics-informed machine learning capabilities for modeling nonlinear dynamics with control and integrates them into a model predictive control framework. To demonstrate the capability of the proposed method we test and validate with two noisy nonlinear dynamic systems: the chaotic Lorenz 3 system, and turning machine tool. Analysis of the results illustrate that the proposed method outperforms state-of-the-art benchmarks as measured by both modeling accuracy and control performance for nonlinear dynamic systems under high-noise conditions.

For many graph-related problems, it can be essential to have a set of structurally diverse graphs. For instance, such graphs can be used for testing graph algorithms or their neural approximations. However, to the best of our knowledge, the problem of generating structurally diverse graphs has not been explored in the literature. In this paper, we fill this gap. First, we discuss how to define diversity for a set of graphs, why this task is non-trivial, and how one can choose a proper diversity measure. Then, for a given diversity measure, we propose and compare several algorithms optimizing it: we consider approaches based on standard random graph models, local graph optimization, genetic algorithms, and neural generative models. We show that it is possible to significantly improve diversity over basic random graph generators. Additionally, our analysis of generated graphs allows us to better understand the properties of graph distances: depending on which diversity measure is used for optimization, the obtained graphs may possess very different structural properties which gives a better understanding of the graph distance underlying the diversity measure.