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Regression experts consistently recommend plotting residuals for model diagnosis, despite the availability of many numerical hypothesis test procedures designed to use residuals to assess problems with a model fit. Here we provide evidence for why this is good advice using data from a visual inference experiment. We show how conventional tests are too sensitive, which means that too often the conclusion would be that the model fit is inadequate. The experiment uses the lineup protocol which puts a residual plot in the context of null plots. This helps generate reliable and consistent reading of residual plots for better model diagnosis. It can also help in an obverse situation where a conventional test would fail to detect a problem with a model due to contaminated data. The lineup protocol also detects a range of departures from good residuals simultaneously. Supplemental materials for the article are available online.

We are interested in building low-dimensional surrogate models to reduce optimization costs, while having theoretical guarantees that the optimum will satisfy the constraints of the full-size model, by making conservative approximations. The surrogate model is constructed using a Gaussian process regression (GPR). To ensure conservativeness, two new approaches are proposed: the first one using bootstrapping, and the second one using concentration inequalities. Those two techniques are based on a stochastic argument and thus will only enforce conservativeness up to a user-defined probability threshold. The method has applications in the context of optimization using the active subspace method for dimensionality reduction of the objective function and the constraints, addressing recorded issues about constraint violations. The resulting algorithms are tested on a toy optimization problem in thermal design.

The Gray-Scott model is a set of reaction-diffusion equations that describes chemical systems far from equilibrium. Interest in this model stems from its ability to generate spatio-temporal structures, including pulses, spots, stripes, and self-replicating patterns. We consider an extension of this model in which the spread of the different chemicals is assumed to be nonlocal, and can thus be represented by an integral operator. In particular, we focus on the case of strictly positive, symmetric, $L^1$ convolution kernels that have a finite second moment. Modeling the equations on a finite interval, we prove the existence of small-time weak solutions in the case of nonlocal Dirichlet and Neumann boundary constraints. We then use this result to develop a finite element numerical scheme that helps us explore the effects of nonlocal diffusion on the formation of pulse solutions.

Models for the dynamics of congestion control generally involve systems of coupled differential equations. Universally, these models assume that traffic sources saturate the maximum transmissions allowed by the congestion control method. This is not suitable for studying congestion control of intermittent but bursty traffic sources. In this paper, we present a characterization of congestion control for arbitrary time-varying traffic that applies to rate-based as well as window-based congestion control. We leverage the capability of network calculus to precisely describe the input-output relationship at network elements for arbitrary source traffic. We show that our characterization can closely track the dynamics of even complex congestion control algorithms.

Out-of-distribution (OOD) detection methods often exploit auxiliary outliers to train model identifying OOD samples, especially discovering challenging outliers from auxiliary outliers dataset to improve OOD detection. However, they may still face limitations in effectively distinguishing between the most challenging OOD samples that are much like in-distribution (ID) data, i.e., \idlike samples. To this end, we propose a novel OOD detection framework that discovers \idlike outliers using CLIP \cite{DBLP:conf/icml/RadfordKHRGASAM21} from the vicinity space of the ID samples, thus helping to identify these most challenging OOD samples. Then a prompt learning framework is proposed that utilizes the identified \idlike outliers to further leverage the capabilities of CLIP for OOD detection. Benefiting from the powerful CLIP, we only need a small number of ID samples to learn the prompts of the model without exposing other auxiliary outlier datasets. By focusing on the most challenging \idlike OOD samples and elegantly exploiting the capabilities of CLIP, our method achieves superior few-shot learning performance on various real-world image datasets (e.g., in 4-shot OOD detection on the ImageNet-1k dataset, our method reduces the average FPR95 by 12.16\% and improves the average AUROC by 2.76\%, compared to state-of-the-art methods). Code is available at //github.com/ycfate/ID-like.

The distribution of objective vectors in a Pareto Front Approximation (PFA) is crucial for representing the associated manifold accurately. Distribution Indicators (DIs) assess the distribution of a PFA numerically, utilizing concepts like distance calculation, Biodiversity, Entropy, Potential Energy, or Clustering. Despite the diversity of DIs, their strengths and weaknesses across assessment scenarios are not well-understood. This paper introduces a taxonomy for classifying DIs, followed by a preference analysis of nine DIs, each representing a category in the taxonomy. Experimental results, considering various PFAs under controlled scenarios (loss of coverage, loss of uniformity, pathological distributions), reveal that some DIs can be misleading and need cautious use. Additionally, DIs based on Biodiversity and Potential Energy show promise for PFA evaluation and comparison of Multi-Objective Evolutionary Algorithms.

Sampling from the output distributions of quantum computations comprising only commuting gates, known as instantaneous quantum polynomial (IQP) computations, is believed to be intractable for classical computers, and hence this task has become a leading candidate for testing the capabilities of quantum devices. Here we demonstrate that for an arbitrary IQP circuit undergoing dephasing or depolarizing noise, whose depth is greater than a critical $O(1)$ threshold, the output distribution can be efficiently sampled by a classical computer. Unlike other simulation algorithms for quantum supremacy tasks, we do not require assumptions on the circuit's architecture, on anti-concentration properties, nor do we require $\Omega(\log(n))$ circuit depth. We take advantage of the fact that IQP circuits have deep sections of diagonal gates, which allows the noise to build up predictably and induce a large-scale breakdown of entanglement within the circuit. Our results suggest that quantum supremacy experiments based on IQP circuits may be more susceptible to classical simulation than previously thought.

Report Noisy Max and Above Threshold are two classical differentially private (DP) selection mechanisms. Their output is obtained by adding noise to a sequence of low-sensitivity queries and reporting the identity of the query whose (noisy) answer satisfies a certain condition. Pure DP guarantees for these mechanisms are easy to obtain when Laplace noise is added to the queries. On the other hand, when instantiated using Gaussian noise, standard analyses only yield approximate DP guarantees despite the fact that the outputs of these mechanisms lie in a discrete space. In this work, we revisit the analysis of Report Noisy Max and Above Threshold with Gaussian noise and show that, under the additional assumption that the underlying queries are bounded, it is possible to provide pure ex-ante DP bounds for Report Noisy Max and pure ex-post DP bounds for Above Threshold. The resulting bounds are tight and depend on closed-form expressions that can be numerically evaluated using standard methods. Empirically we find these lead to tighter privacy accounting in the high privacy, low data regime. Further, we propose a simple privacy filter for composing pure ex-post DP guarantees, and use it to derive a fully adaptive Gaussian Sparse Vector Technique mechanism. Finally, we provide experiments on mobility and energy consumption datasets demonstrating that our Sparse Vector Technique is practically competitive with previous approaches and requires less hyper-parameter tuning.

In many applications, a combinatorial problem must be repeatedly solved with similar, but distinct parameters. Yet, the parameters $w$ are not directly observed; only contextual data $d$ that correlates with $w$ is available. It is tempting to use a neural network to predict $w$ given $d$. However, training such a model requires reconciling the discrete nature of combinatorial optimization with the gradient-based frameworks used to train neural networks. When the problem in question is an Integer Linear Program (ILP), one approach to overcome this training issue is to consider a continuous relaxation of the combinatorial problem. While existing methods utilizing this approach have shown to be highly effective on small problems, they do not always scale well to large problems. In this work, we draw on ideas from modern convex optimization to design a network and training scheme which scales effortlessly to problems with thousands of variables. Our experiments verify the computational advantage our proposed method enjoys on two representative problems, namely the shortest path problem and the knapsack problem.

We consider a nonparametric regression model with continuous endogenous independent variables when only discrete instruments are available that are independent of the error term. While this framework is very relevant for applied research, its implementation is cumbersome, as the regression function becomes the solution to a nonlinear integral equation. We propose a simple iterative procedure to estimate such models and showcase some of its asymptotic properties. In a simulation experiment, we discuss the details of its implementation in the case when the instrumental variable is binary. We conclude with an empirical application in which we examine the effect of pollution on house prices in a short panel of U.S. counties.