arXiv subjects

Dave Zachariah

Publications and source records attributed to Dave Zachariah.

At least 37 records · Page 2Linked to original sources

arXiv2022

Calibration tests beyond classification

Most supervised machine learning tasks are subject to irreducible prediction errors. Probabilistic predictive models address this limitation by providing probability distributions that represent a belief over plausible targets, rather than point estimates. Such models can be a valuable tool in decision-making under uncertainty, provided that the model output is meaningful and interpretable. Calibrated models guarantee that the probabilistic predictions are neither over- nor under-confident. In the machine learning literature, different measures and statistical tests have been proposed and studied for evaluating the calibration of classification models. For regression problems, however, research has been focused on a weaker condition of calibration based on predicted quantiles for real-valued targets. In this paper, we propose the first framework that unifies calibration evaluation and tests for general probabilistic predictive models. It applies to any such model, including classification and regression models of arbitrary dimension. Furthermore, the framework generalizes existing measures and provides a more intuitive reformulation of a recently proposed framework for calibration in multi-class classification. In particular, we reformulate and generalize the kernel calibration error, its estimators, and hypothesis tests using scalar-valued kernels, and evaluate the calibration of real-valued regression problems.

stat.ML↗

arXiv2022

Surprises in adversarially-trained linear regression

State-of-the-art machine learning models can be vulnerable to very small input perturbations that are adversarially constructed. Adversarial training is an effective approach to defend against such examples. It is formulated as a min-max problem, searching for the best solution when the training data was corrupted by the worst-case attacks. For linear regression problems, adversarial training can be formulated as a convex problem. We use this reformulation to make two technical contributions: First, we formulate the training problem as an instance of robust regression to reveal its connection to parameter-shrinking methods, specifically that $\ell_\infty$-adversarial training produces sparse solutions. Secondly, we study adversarial training in the overparameterized regime, i.e. when there are more parameters than data. We prove that adversarial training with small disturbances gives the solution with the minimum-norm that interpolates the training data. Ridge regression and lasso approximate such interpolating solutions as their regularization parameter vanishes. By contrast, for adversarial training, the transition into the interpolation regime is abrupt and for non-zero values of disturbance. This result is proved and illustrated with numerical examples.

stat.ML↗

arXiv2022

Robust Learning in Heterogeneous Contexts

We consider the problem of learning from training data obtained in different contexts, where the underlying context distribution is unknown and is estimated empirically. We develop a robust method that takes into account the uncertainty of the context distribution. Unlike the conventional and overly conservative minimax approach, we focus on excess risks and construct distribution sets with statistical coverage to achieve an appropriate trade-off between performance and robustness. The proposed method is computationally scalable and shown to interpolate between empirical risk minimization and minimax regret objectives. Using both real and synthetic data, we demonstrate its ability to provide robustness in worst-case scenarios without harming performance in the nominal scenario.

stat.ML↗

arXiv2022

Tuned Regularized Estimators for Linear Regression via Covariance Fitting

We consider the problem of finding tuned regularized parameter estimators for linear models. We start by showing that three known optimal linear estimators belong to a wider class of estimators that can be formulated as a solution to a weighted and constrained minimization problem. The optimal weights, however, are typically unknown in many applications. This begs the question, how should we choose the weights using only the data? We propose using the covariance fitting SPICE-methodology to obtain data-adaptive weights and show that the resulting class of estimators yields tuned versions of known regularized estimators - such as ridge regression, LASSO, and regularized least absolute deviation. These theoretical results unify several important estimators under a common umbrella. The resulting tuned estimators are also shown to be practically relevant by means of a number of numerical examples.

math.ST↗

arXiv2021

Learning Pareto-Efficient Decisions with Confidence

The paper considers the problem of multi-objective decision support when outcomes are uncertain. We extend the concept of Pareto-efficient decisions to take into account the uncertainty of decision outcomes across varying contexts. This enables quantifying trade-offs between decisions in terms of tail outcomes that are relevant in safety-critical applications. We propose a method for learning efficient decisions with statistical confidence, building on results from the conformal prediction literature. The method adapts to weak or nonexistent context covariate overlap and its statistical guarantees are evaluated using both synthetic and real data.

stat.ML↗

arXiv2021

Inference of Causal Effects when Control Variables are Unknown

Conventional methods in causal effect inferencetypically rely on specifying a valid set of control variables. When this set is unknown or misspecified, inferences will be erroneous. We propose a method for inferring average causal effects when all potential confounders are observed, but thecontrol variables are unknown. When the data-generating process belongs to the class of acyclical linear structural causal models, we prove that themethod yields asymptotically valid confidence intervals. Our results build upon a smooth characterization of linear directed acyclic graphs. We verify the capability of the method to produce valid confidence intervals for average causal effects using synthetic data, even when the appropriate specification of control variables is unknown.

stat.ME↗

arXiv2021

Robust Localization in Wireless Networks From Corrupted Signals

We address the problem of timing-based localization in wireless networks, when an unknown fraction of data is corrupted by nonideal signal conditions. While timing-based techniques enable accurate localization, they are also sensitive to such corrupted data. We develop a robust method that is applicable to a range of localization techniques, including time-of-arrival, time-difference-of-arrival and time-difference in schedule-based transmissions. The method is nonparametric and requires only an upper bound on the fraction of corrupted data, thus obviating distributional assumptions of the corrupting noise distribution. The robustness of the method is demonstrated in numerical experiments.

cs.IT↗

arXiv2020

Prediction of Spatial Point Processes: Regularized Method with Out-of-Sample Guarantees

A spatial point process can be characterized by an intensity function which predicts the number of events that occur across space. In this paper, we develop a method to infer predictive intensity intervals by learning a spatial model using a regularized criterion. We prove that the proposed method exhibits out-of-sample prediction performance guarantees which, unlike standard estimators, are valid even when the spatial model is misspecified. The method is demonstrated using synthetic as well as real spatial data.

stat.ML↗

arXiv2020

Learning Robust Decision Policies from Observational Data

We address the problem of learning a decision policy from observational data of past decisions in contexts with features and associated outcomes. The past policy maybe unknown and in safety-critical applications, such as medical decision support, it is of interest to learn robust policies that reduce the risk of outcomes with high costs. In this paper, we develop a method for learning policies that reduce tails of the cost distribution at a specified level and, moreover, provide a statistically valid bound on the cost of each decision. These properties are valid under finite samples -- even in scenarios with uneven or no overlap between features for different decisions in the observed data -- by building on recent results in conformal prediction. The performance and statistical properties of the proposed method are illustrated using both real and synthetic data.

cs.LG↗

arXiv2020

Robust Prediction when Features are Missing

Predictors are learned using past training data which may contain features that are unavailable at the time of prediction. We develop an approach that is robust against outlying missing features, based on the optimality properties of an oracle predictor which observes them. The robustness properties of the approach are demonstrated on both real and synthetic data.

eess.SP↗

arXiv2020

Calibration tests in multi-class classification: A unifying framework

In safety-critical applications a probabilistic model is usually required to be calibrated, i.e., to capture the uncertainty of its predictions accurately. In multi-class classification, calibration of the most confident predictions only is often not sufficient. We propose and study calibration measures for multi-class classification that generalize existing measures such as the expected calibration error, the maximum calibration error, and the maximum mean calibration error. We propose and evaluate empirically different consistent and unbiased estimators for a specific class of measures based on matrix-valued kernels. Importantly, these estimators can be interpreted as test statistics associated with well-defined bounds and approximations of the p-value under the null hypothesis that the model is calibrated, significantly improving the interpretability of calibration measures, which otherwise lack any meaningful unit or scale.

stat.ML↗

arXiv2020

A latent variable approach to heat load prediction in thermal grids

In this paper a new method for heat load prediction in district energy systems is proposed. The method uses a nominal model for the prediction of the outdoor temperature dependent space heating load, and a data driven latent variable model to predict the time dependent residual heat load. The residual heat load arises mainly from time dependent operation of space heating and ventilation, and domestic hot water production. The resulting model is recursively updated on the basis of a hyper-parameter free implementation that results in a parsimonious model allowing for high computational performance. The approach is applied to a single multi-dwelling building in Lulea, Sweden, predicting the heat load using a relatively small number of model parameters and easily obtained measurements. The results are compared with predictions using an artificial neural network, showing that the proposed method achieves better prediction accuracy for the validation case. Additionally, the proposed methods exhibits explainable behavior through the use of an interpretable physical model.

eess.SP↗

arXiv2020

Robust Risk Minimization for Statistical Learning

We consider a general statistical learning problem where an unknown fraction of the training data is corrupted. We develop a robust learning method that only requires specifying an upper bound on the corrupted data fraction. The method minimizes a risk function defined by a non-parametric distribution with unknown probability weights. We derive and analyse the optimal weights and show how they provide robustness against corrupted data. Furthermore, we give a computationally efficient coordinate descent algorithm to solve the risk minimization problem. We demonstrate the wide range applicability of the method, including regression, classification, unsupervised learning and classic parameter estimation, with state-of-the-art performance.

stat.ML↗

arXiv2019

Effect Inference from Two-Group Data with Sampling Bias

In many applications, different populations are compared using data that are sampled in a biased manner. Under sampling biases, standard methods that estimate the difference between the population means yield unreliable inferences. Here we develop an inference method that is resilient to sampling biases and is able to control the false positive errors under moderate bias levels in contrast to the standard approach. We demonstrate the method using synthetic and real biomarker data.

math.ST↗

arXiv2019

Reliable Semi-Supervised Learning when Labels are Missing at Random

Semi-supervised learning methods are motivated by the availability of large datasets with unlabeled features in addition to labeled data. Unlabeled data is, however, not guaranteed to improve classification performance and has in fact been reported to impair the performance in certain cases. A fundamental source of error arises from restrictive assumptions about the unlabeled features, which result in unreliable classifiers that underestimate their prediction error probabilities. In this paper, we develop a semi-supervised learning approach that relaxes such assumptions and is capable of providing classifiers that reliably quantify the label uncertainty. The approach is applicable using any generative model with a supervised learning algorithm. We illustrate the approach using both handwritten digit and cloth classification data where the labels are missing at random.

stat.ML↗

arXiv2019

Inferring Heterogeneous Causal Effects in Presence of Spatial Confounding

We address the problem of inferring the causal effect of an exposure on an outcome across space, using observational data. The data is possibly subject to unmeasured confounding variables which, in a standard approach, must be adjusted for by estimating a nuisance function. Here we develop a method that eliminates the nuisance function, while mitigating the resulting errors-in-variables. The result is a robust and accurate inference method for spatially varying heterogeneous causal effects. The properties of the method are demonstrated on synthetic as well as real data from Germany and the US.

stat.ME↗

arXiv2019

Data Consistency Approach to Model Validation

In scientific inference problems, the underlying statistical modeling assumptions have a crucial impact on the end results. There exist, however, only a few automatic means for validating these fundamental modelling assumptions. The contribution in this paper is a general criterion to evaluate the consistency of a set of statistical models with respect to observed data. This is achieved by automatically gauging the models' ability to generate data that is similar to the observed data. Importantly, the criterion follows from the model class itself and is therefore directly applicable to a broad range of inference problems with varying data types, ranging from independent univariate data to high-dimensional time-series. The proposed data consistency criterion is illustrated, evaluated and compared to several well-established methods using three synthetic and two real data sets.

stat.ME↗

arXiv2018

Learning Sparse Graphs for Prediction and Filtering of Multivariate Data Processes

We address the problem of prediction of multivariate data process using an underlying graph model. We develop a method that learns a sparse partial correlation graph in a tuning-free and computationally efficient manner. Specifically, the graph structure is learned recursively without the need for cross-validation or parameter tuning by building upon a hyperparameter-free framework. Our approach does not require the graph to be undirected and also accommodates varying noise levels across different nodes.Experiments using real-world datasets show that the proposed method offers significant performance gains in prediction, in comparison with the graphs frequently associated with these datasets.

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