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<p>Motivated by time series forecasting, we study Online Linear Optimization (OLO) under the coupling of two problem structures: the domain is unbounded, and the performance of an algorithm is measured by its dynamic regret. Handling either of them requires the regret bound to depend on certain complexity measure of the comparator sequence -- specifically, the comparator norm in unconstrained OLO, and the path length in dynamic regret. In contrast to a recent work (Jacobsen & Cutkosky, 2022) that adapts to the combination of these two complexity measures, we propose an alternative complexity measure by recasting the problem into sparse…
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Latest: Feb. 4, 2023, 11:04 p.m.
<p>Generative models can have distinct mode of failures like mode dropping and low quality samples, which cannot be captured by a single scalar metric. To address this, recent works propose evaluating generative models using precision and recall, where precision measures quality of samples and recall measures the coverage of the target distribution. Although a variety of discrepancy measures between the target and estimated distribution are used to train generative models, it is unclear what precision-recall trade-offs are achieved by various choices of the discrepancy measures. In this paper, we show that achieving a specified precision-recal…
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<p>The constantly expanding frequency and loss affected by natural disasters pose a severe challenge to the traditional catastrophe insurance market. This paper aims to develop an innovative framework of pricing catastrophic bonds triggered by multiple events with extreme dependence structure. Given the low contingency of the bond's cash flows and high return, the multiple-event CAT bond may successfully transfer the catastrophe risk to the big financial markets meeting the diversification of capital allocations for most potential investors. The designed hybrid trigger mechanism helps reduce moral hazard and improve bond attractiveness wi…
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<p>Extended cure survival models enable to separate covariates that affect the probability of an event (or `long-term' survival) from those only affecting the event timing (or `short-term' survival). We propose to generalize the bounded cumulative hazard model to handle additive terms for time-varying (exogenous) covariates jointly impacting long- and short-term survival. The selection of the penalty parameters is a challenge in that framework. A fast algorithm based on Laplace approximations in Bayesian P-spline models is proposed. The methodology is motivated by fertility studies where women's characteristics such as the emplo…
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<p>The Causality field aims to find systematic methods for uncovering cause-effect relationships. Such methods can find applications in many research fields, justifying a great interest in this domain. Machine Learning models have shown success in a large variety of tasks by extracting correlation patterns from high-dimensional data but still struggle when generalizing out of their initial distribution. As causal engines aim to learn mechanisms that are independent from a data distribution, combining Machine Learning with Causality has the potential to bring benefits to the two fields. In our work, we motivate this assumption and provide appli…
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<p>Two-sample testing tests whether the distributions generating two samples are identical. We pose the two-sample testing problem in a new scenario where the sample measurements (or sample features) are inexpensive to access, but their group memberships (or labels) are costly. We devise the first \emph{active sequential two-sample testing framework} that not only sequentially but also \emph{actively queries} sample labels to address the problem. Our test statistic is a likelihood ratio where one likelihood is found by maximization over all class priors, and the other is given by a classification model. The classification model is adaptively u…
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<p>Assortment optimization has received active explorations in the past few decades due to its practical importance. Despite the extensive literature dealing with optimization algorithms and latent score estimation, uncertainty quantification for the optimal assortment still needs to be explored and is of great practical significance. Instead of estimating and recovering the complete optimal offer set, decision-makers may only be interested in testing whether a given property holds true for the optimal assortment, such as whether they should include several products of interest in the optimal set, or how many categories of products the optimal…
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<p>We introduce prediction-powered inference $\unicode{x2013}$ a framework for performing valid statistical inference when an experimental data set is supplemented with predictions from a machine-learning system. Our framework yields provably valid conclusions without making any assumptions on the machine-learning algorithm that supplies the predictions. Higher accuracy of the predictions translates to smaller confidence intervals, permitting more powerful inference. Prediction-powered inference yields simple algorithms for computing valid confidence intervals for statistical objects such as means, quantiles, and linear and logistic regression…
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<p>Off-policy evaluation (OPE) is a method for estimating the return of a target policy using some pre-collected observational data generated by a potentially different behavior policy. In some cases, there may be unmeasured variables that can confound the action-reward or action-next-state relationships, rendering many existing OPE approaches ineffective. This paper develops an instrumental variable (IV)-based method for consistent OPE in confounded Markov decision processes (MDPs). Similar to single-stage decision making, we show that IV enables us to correctly identify the target policy's value in infinite horizon settings as well. Fur…
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<p>Economists frequently estimate average treatment effects (ATEs) for transformations of the outcome that are well-defined at zero but behave like $\log(y)$ when $y$ is large (e.g., $\log(1+y)$, $\mathrm{arcsinh}(y)$). We show that these ATEs depend arbitrarily on the units of the outcome, and thus cannot be interpreted as percentage effects. Moreover, we prove that when the outcome can equal zero, there is no parameter of the form $E_P[g(Y(1),Y(0))]$ that is point-identified and unit-invariant. We discuss sensible alternative target parameters for settings with zero-valued outcomes that relax at least one of these requirements. </p&am…
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<p>Many industrial applications rely on real-time optimization to improve key performance indicators. In the case of unknown process characteristics, real-time optimization becomes challenging, particularly for the satisfaction of safety constraints. In this paper, we demonstrate the application of an adaptive and explorative real-time optimization framework to an industrial refrigeration process, where we learn the process characteristics through changes in process control targets and through exploration to satisfy safety constraints. We quantify the uncertainty in unknown compressor characteristics of the refrigeration plant by using Gaussia…
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<p>Performance of machine learning models may differ between training and deployment for many reasons. For instance, model performance can change between environments due to changes in data quality, observing a different population than the one in training, or changes in the relationship between labels and features. These changes result in distribution shifts across environments. Attributing model performance changes to specific shifts is critical for identifying sources of model failures, and for taking mitigating actions that ensure robust models. In this work, we introduce the problem of attributing performance differences between environme…
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<p>This paper studies a semiparametric quantile regression model with endogenous variables and random right censoring. The endogeneity issue is solved using instrumental variables. It is assumed that the structural quantile of the logarithm of the outcome variable is linear in the covariates and censoring is independent. The regressors and instruments can be either continuous or discrete. The specification generates a continuum of equations of which the quantile regression coefficients are a solution. Identification is obtained when this system of equations has a unique solution. Our estimation procedure solves an empirical analogue of the sys…
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<p>We expect the generalization error to improve with more samples from a similar task, and to deteriorate with more samples from an out-of-distribution (OOD) task. In this work, we show a counter-intuitive phenomenon: the generalization error of a task can be a non-monotonic function of the number of OOD samples. As the number of OOD samples increases, the generalization error on the target task improves before deteriorating beyond a threshold. In other words, there is value in training on small amounts of OOD data. We use Fisher's Linear Discriminant on synthetic datasets and deep networks on computer vision benchmarks such as MNIST, CI…
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<p>This paper proposes a data-driven approximate Bayesian computation framework for parameter estimation and uncertainty quantification of epidemic models, which incorporates two novelties: (i) the identification of the initial conditions by using plausible dynamic states that are compatible with observational data; (ii) learning of an informative prior distribution for the model parameters via the cross-entropy method. The new methodology's effectiveness is illustrated with the aid of actual data from the COVID-19 epidemic in Rio de Janeiro city in Brazil, employing an ordinary differential equation-based model with a generalized SEIR me…
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<p>Substandard and falsified pharmaceuticals, prevalent in low- and middle-income countries, substantially increase levels of morbidity, mortality and drug resistance. Regulatory agencies combat this problem using post-market surveillance by collecting and testing samples where consumers purchase products. Existing analysis tools for post-market surveillance data focus attention on the locations of positive samples. This paper looks to expand such analysis through underutilized supply-chain information to provide inference on sources of substandard and falsified products. We first establish the presence of unidentifiability issues when integra…
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<p>Maximum likelihood estimation in logistic regression with mixed effects is known to often result in estimates on the boundary of the parameter space. Such estimates, which include infinite values for fixed effects and singular or infinite variance components, can cause havoc to numerical estimation procedures and inference. We introduce an appropriately scaled additive penalty to the log-likelihood function, or an approximation thereof, which penalizes the fixed effects by the Jeffreys' invariant prior for the model with no random effects and the variance components by a composition of negative Huber loss functions. The resulting maxim…
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<p>Concept Bottleneck Models (CBMs) map the inputs onto a set of interpretable concepts (``the bottleneck'') and use the concepts to make predictions. A concept bottleneck enhances interpretability since it can be investigated to understand what concepts the model "sees" in an input and which of these concepts are deemed important. However, CBMs are restrictive in practice as they require dense concept annotations in the training data to learn the bottleneck. Moreover, CBMs often do not match the accuracy of an unrestricted neural network, reducing the incentive to deploy them in practice. In this work, we address these lim…
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<p>Optimal designs minimize the number of experimental runs (samples) needed to accurately estimate model parameters, resulting in algorithms that, for instance, efficiently minimize parameter estimate variance. Governed by knowledge of past observations, adaptive approaches adjust sampling constraints online as model parameter estimates are refined, continually maximizing expected information gained or variance reduced. We apply adaptive Bayesian inference to estimate transition rates of Markov chains, a common class of models for stochastic processes in nature. Unlike most previous studies, our sequential Bayesian optimal design is updated w…
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<p>We study the dynamics and implicit bias of gradient flow (GF) on univariate ReLU neural networks with a single hidden layer in a binary classification setting. We show that when the labels are determined by the sign of a target network with $r$ neurons, with high probability over the initialization of the network and the sampling of the dataset, GF converges in direction (suitably defined) to a network achieving perfect training accuracy and having at most $\mathcal{O}(r)$ linear regions, implying a generalization bound. Unlike many other results in the literature, under an additional assumption on the distribution of the data, our result h…
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<p>Using gradient descent (GD) with fixed or decaying step-size is a standard practice in unconstrained optimization problems. However, when the loss function is only locally convex, such a step-size schedule artificially slows GD down as it cannot explore the flat curvature of the loss function. To overcome that issue, we propose to exponentially increase the step-size of the GD algorithm. Under homogeneous assumptions on the loss function, we demonstrate that the iterates of the proposed \emph{exponential step size gradient descent} (EGD) algorithm converge linearly to the optimal solution. Leveraging that optimization insight, we then consi…
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<p>In a round-robin tournament, a team may lack the incentive to win if its final rank does not depend on the outcome of the matches still to be played. This paper introduces a classification scheme to determine these weakly (where one team is indifferent) or strongly (where both teams are indifferent) stakeless matches in a double round-robin contest with four teams. The probability that such matches arise can serve as a novel fairness criterion to compare and evaluate match schedules. Our approach is illustrated by the UEFA Champions League group stage. A simulation model is built to compare the 12 valid schedules for the group matches. Some…
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<p>A fundamental question in designing lossy data compression schemes is how well one can do in comparison with the rate-distortion function, which describes the known theoretical limits of lossy compression. Motivated by the empirical success of deep neural network (DNN) compressors on large, real-world data, we investigate methods to estimate the rate-distortion function on such data, which would allow comparison of DNN compressors with optimality. While one could use the empirical distribution of the data and apply the Blahut-Arimoto algorithm, this approach presents several computational challenges and inaccuracies when the datasets are la…
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<p>A lot of studies on the summary measures of predictive strength of categorical response models consider the likelihood ratio index (LRI), also known as the McFadden-$R^2$, a better option than many other measures. We propose a simple modification of the LRI that adjusts for the effect of the number of response categories on the measure and that also rescales its values, mimicking an underlying latent measure. The modified measure is applicable to both binary and ordinal response models fitted by maximum likelihood. Results from simulation studies and a real data example on the olfactory perception of boar taint show that the proposed measur…
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<p>Many models for point process data are defined through a thinning procedure where locations of a base process (often Poisson) are either kept (observed) or discarded (thinned). In this paper, we go back to the fundamentals of the distribution theory for point processes and provide a colouring theorem that characterizes the joint density of thinned and observed locations in any of such models. In practice, the marginal model of observed points is often intractable, but thinned locations can be instantiated from their conditional distribution and typical data augmentation schemes can be employed to circumvent this problem. Such approaches hav…
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