Latest research revealed a considerable lack of reliability within user feedback and discussed striking impacts for the assessment of adaptive web systems and content personalisation approaches, e.g. ranking errors, systematic biases to accuracy metrics as well as its natural offset (the magic barrier). In order to perform holistic assessments and to improve web systems, a variety of strategies have been proposed to deal with this so-called human uncertainty. In this contribution we discuss the most relevant strategies to handle uncertain feedback and demonstrate that these approaches are more or less ineffective to fulfil their objectives. In doing so, we consider human uncertainty within a purely probabilistic framework and utilise hypothesis testing as well as a generalisation of the magic barrier to compare the effects of recently proposed algorithms. On this basis we recommend a novel strategy of acceptance which turns away from mere filtering and discuss potential benefits for the community of the WWW.
This paper studies the problem of distributed classification with a network of heterogeneous agents. The agents seek to jointly identify the underlying target class that best describes a sequence of observations. The problem is first abstracted to a hypothesis-testing framework, where we assume that the agents seek to agree on the hypothesis (target class) that best matches the distribution of observations. Non-Bayesian social learning theory provides a framework that solves this problem in an efficient manner by allowing the agents to sequentially communicate and update their beliefs for each hypothesis over the network. Most existing approaches assume that agents have access to exact statistical models for each hypothesis. However, in many practical applications, agents learn the likelihood models based on limited data, which induces uncertainty in the likelihood function parameters. In this work, we build upon the concept of uncertain models to incorporate the agents' uncertainty in the likelihoods by identifying a broad set of parametric distribution that allows the agents' beliefs to converge to the same result as a centralized approach. Furthermore, we empirically explore extensions to non-parametric models to provide a generalized framework of uncertain models in non-Bayesian social learning.
Machine learning models are vulnerable to adversarial attacks that can often cause misclassification by introducing small but well designed perturbations. In this paper, we explore, in the setting of classical composite hypothesis testing, a defense strategy based on the generalized likelihood ratio test (GLRT), which jointly estimates the class of interest and the adversarial perturbation. We evaluate the GLRT approach for the special case of binary hypothesis testing in white Gaussian noise under $\ell_{\infty}$ norm-bounded adversarial perturbations, a setting for which a minimax strategy optimizing for the worst-case attack is known. We show that the GLRT approach yields performance competitive with that of the minimax approach under the worst-case attack, and observe that it yields a better robustness-accuracy trade-off under weaker attacks, depending on the values of signal components relative to the attack budget. We also observe that the GLRT defense generalizes naturally to more complex models for which optimal minimax classifiers are not known.
This paper studies experimental designs for estimation and inference on policies with spillover effects. Units are organized into a finite number of large clusters and interact in unknown ways within each cluster. First, we introduce a single-wave experiment that, by varying the randomization across cluster pairs, estimates the marginal effect of a change in treatment probabilities, taking spillover effects into account. Using the marginal effect, we propose a test for policy optimality. Second, we design a multiple-wave experiment to estimate welfare-maximizing treatment rules. We provide strong theoretical guarantees and an implementation in a large-scale field experiment.
Information bottleneck (IB) and privacy funnel (PF) are two closely related optimization problems which have found applications in machine learning, design of privacy algorithms, capacity problems (e.g., Mrs. Gerber's Lemma), strong data processing inequalities, among others. In this work, we first investigate the functional properties of IB and PF through a unified theoretical framework. We then connect them to three information-theoretic coding problems, namely hypothesis testing against independence, noisy source coding and dependence dilution. Leveraging these connections, we prove a new cardinality bound for the auxiliary variable in IB, making its computation more tractable for discrete random variables. In the second part, we introduce a general family of optimization problems, termed as \textit{bottleneck problems}, by replacing mutual information in IB and PF with other notions of mutual information, namely $f$-information and Arimoto's mutual information. We then argue that, unlike IB and PF, these problems lead to easily interpretable guarantee in a variety of inference tasks with statistical constraints on accuracy and privacy. Although the underlying optimization problems are non-convex, we develop a technique to evaluate bottleneck problems in closed form by equivalently expressing them in terms of lower convex or upper concave envelope of certain functions. By applying this technique to binary case, we derive closed form expressions for several bottleneck problems.
Classical asymptotic theory for statistical inference usually involves calibrating a statistic by fixing the dimension $d$ while letting the sample size $n$ increase to infinity. Recently, much effort has been dedicated towards understanding how these methods behave in high-dimensional settings, where $d$ and $n$ both increase to infinity together. This often leads to different inference procedures, depending on the assumptions about the dimensionality, leaving the practitioner in a bind: given a dataset with 100 samples in 20 dimensions, should they calibrate by assuming $n \gg d$, or $d/n \approx 0.2$? This paper considers the goal of dimension-agnostic inference; developing methods whose validity does not depend on any assumption on $d$ versus $n$. We introduce an approach that uses variational representations of existing test statistics along with sample splitting and self-normalization to produce a refined test statistic with a Gaussian limiting distribution, regardless of how $d$ scales with $n$. The resulting statistic can be viewed as a careful modification of degenerate U-statistics, dropping diagonal blocks and retaining off-diagonal blocks. We exemplify our technique for some classical problems including one-sample mean and covariance testing, and show that our tests have minimax rate-optimal power against appropriate local alternatives. In most settings, our cross U-statistic matches the high-dimensional power of the corresponding (degenerate) U-statistic up to a $\sqrt{2}$ factor.
Linear Mixed Effects (LME) models have been widely applied in clustered data analysis in many areas including marketing research, clinical trials, and biomedical studies. Inference can be conducted using maximum likelihood approach if assuming Normal distributions on the random effects. However, in many applications of economy, business and medicine, it is often essential to impose constraints on the regression parameters after taking their real-world interpretations into account. Therefore, in this paper we extend the classical (unconstrained) LME models to allow for sign constraints on its overall coefficients. We propose to assume a symmetric doubly truncated Normal (SDTN) distribution on the random effects instead of the unconstrained Normal distribution which is often found in classical literature. With the aforementioned change, difficulty has dramatically increased as the exact distribution of the dependent variable becomes analytically intractable. We then develop likelihood-based approaches to estimate the unknown model parameters utilizing the approximation of its exact distribution. Simulation studies have shown that the proposed constrained model not only improves real-world interpretations of results, but also achieves satisfactory performance on model fits as compared to the existing model.
A pervasive issue in statistical hypothesis testing is that the reported $p$-values are biased downward by data "peeking" -- the practice of reporting only progressively extreme values of the test statistic as more data samples are collected. We develop principled mechanisms to estimate such running extrema of test statistics, which directly address the effect of peeking in some general scenarios.
We propose a simple robust hypothesis test that has the same sample complexity as that of the optimal Neyman-Pearson test up to constants, but robust to distribution perturbations under Hellinger distance. We discuss the applicability of such a robust test for estimating distributions in Hellinger distance. We empirically demonstrate the power of the test on canonical distributions.
Collections of probability distributions arise in a variety of applications ranging from user activity pattern analysis to brain connectomics. In practice these distributions can be defined over diverse domain types including finite intervals, circles, cylinders, spheres, other manifolds, and graphs. This paper introduces an approach for detecting differences between two collections of distributions over such general domains. To this end, we propose the intrinsic slicing construction that yields a novel class of Wasserstein distances on manifolds and graphs. These distances are Hilbert embeddable, allowing us to reduce the distribution collection comparison problem to a more familiar mean testing problem in a Hilbert space. We provide two testing procedures one based on resampling and another on combining p-values from coordinate-wise tests. Our experiments in various synthetic and real data settings show that the resulting tests are powerful and the p-values are well-calibrated.
Many real-world sequential decision-making problems involve critical systems with financial risks and human-life risks. While several works in the past have proposed methods that are safe for deployment, they assume that the underlying problem is stationary. However, many real-world problems of interest exhibit non-stationarity, and when stakes are high, the cost associated with a false stationarity assumption may be unacceptable. We take the first steps towards ensuring safety, with high confidence, for smoothly-varying non-stationary decision problems. Our proposed method extends a type of safe algorithm, called a Seldonian algorithm, through a synthesis of model-free reinforcement learning with time-series analysis. Safety is ensured using sequential hypothesis testing of a policy's forecasted performance, and confidence intervals are obtained using wild bootstrap.
In many RL applications, once training ends, it is vital to detect any deterioration in the agent performance as soon as possible. Furthermore, it often has to be done without modifying the policy and under minimal assumptions regarding the environment. In this paper, we address this problem by focusing directly on the rewards and testing for degradation. We consider an episodic framework, where the rewards within each episode are not independent, nor identically-distributed, nor Markov. We present this problem as a multivariate mean-shift detection problem with possibly partial observations. We define the mean-shift in a way corresponding to deterioration of a temporal signal (such as the rewards), and derive a test for this problem with optimal statistical power. Empirically, on deteriorated rewards in control problems (generated using various environment modifications), the test is demonstrated to be more powerful than standard tests - often by orders of magnitude. We also suggest a novel Bootstrap mechanism for False Alarm Rate control (BFAR), applicable to episodic (non-i.i.d) signal and allowing our test to run sequentially in an online manner. Our method does not rely on a learned model of the environment, is entirely external to the agent, and in fact can be applied to detect changes or drifts in any episodic signal.
This paper introduces an automated vision system for animal detection in trail-camera images taken from a field under the administration of the Texas Parks and Wildlife Department. As traditional wildlife counting techniques are intrusive and labor intensive to conduct, trail-camera imaging is a comparatively non-intrusive method for capturing wildlife activity. However, given the large volume of images produced from trail-cameras, manual analysis of the images remains time-consuming and inefficient. We implemented a two-stage deep convolutional neural network pipeline to find animal-containing images in the first stage and then process these images to detect birds in the second stage. The animal classification system classifies animal images with overall 93% sensitivity and 96% specificity. The bird detection system achieves better than 93% sensitivity, 92% specificity, and 68% average Intersection-over-Union rate. The entire pipeline processes an image in less than 0.5 seconds as opposed to an average 30 seconds for a human labeler. We also addressed post-deployment issues related to data drift for the animal classification system as image features vary with seasonal changes. This system utilizes an automatic retraining algorithm to detect data drift and update the system. We introduce a novel technique for detecting drifted images and triggering the retraining procedure. Two statistical experiments are also presented to explain the prediction behavior of the animal classification system. These experiments investigate the cues that steers the system towards a particular decision. Statistical hypothesis testing demonstrates that the presence of an animal in the input image significantly contributes to the system's decisions.
The traditional binary classification framework constructs classifiers which may have good accuracy, but whose false positive and false negative error rates are not under users' control. In many cases, one of the errors is more severe and only the classifiers with the corresponding rate lower than the predefined threshold are acceptable. In this study, we combine binary classification with statistical hypothesis testing to control the target error rate of already trained classifiers. In particular, we show how to turn binary classifiers into statistical tests, calculate the classification p-values, and use them to limit the target error rate.
Work in information retrieval has largely been centered around ranking and relevance: given a query, return some number of results ordered by relevance to the user. The problem of result list truncation, or where to truncate the ranked list of results, however, has received less attention despite being crucial in a variety of applications. Such truncation is a balancing act between the overall relevance, or usefulness of the results, with the user cost of processing more results. Result list truncation can be challenging because relevance scores are often not well-calibrated. This is particularly true in large-scale IR systems where documents and queries are embedded in the same metric space and a query's nearest document neighbors are returned during inference. Here, relevance is inversely proportional to the distance between the query and candidate document, but what distance constitutes relevance varies from query to query and changes dynamically as more documents are added to the index. In this work, we propose Surprise scoring, a statistical method that leverages the Generalized Pareto distribution that arises in extreme value theory to produce interpretable and calibrated relevance scores at query time using nothing more than the ranked scores. We demonstrate its effectiveness on the result list truncation task across image, text, and IR datasets and compare it to both classical and recent baselines. We draw connections to hypothesis testing and $p$-values.
Quantum hypothesis testing is one of the most fundamental problems in quantum information theory, with crucial implications in areas like quantum sensing, where it has been used to prove quantum advantage in a series of binary photonic protocols, e.g., for target detection or memory cell readout. In this work, we generalize this theoretical model to the multi-partite setting of barcode decoding and pattern recognition. We start by defining a digital image as an array or grid of pixels, each pixel corresponding to an ensemble of quantum channels. Specializing each pixel to a black and white alphabet, we naturally define an optical model of barcode. In this scenario, we show that the use of quantum entangled sources, combined with suitable measurements and data processing, greatly outperforms classical coherent-state strategies for the tasks of barcode data decoding and classification of black and white patterns. Moreover, introducing relevant bounds, we show that the problem of pattern recognition is significantly simpler than barcode decoding, as long as the minimum Hamming distance between images from different classes is large enough. Finally, we theoretically demonstrate the advantage of using quantum sensors for pattern recognition with the nearest neighbor classifier, a supervised learning algorithm, and numerically verify this prediction for handwritten digit classification.
Although deep neural networks are effective on supervised learning tasks, they have been shown to be brittle. They are prone to overfitting on their training distribution and are easily fooled by small adversarial perturbations. In this paper, we leverage generative models to identify and characterize instances where classifiers fail to generalize. We propose a generative model of the features extracted by a classifier, and show using rigorous hypothesis testing that errors tend to occur when features are assigned low-probability by our model. From this observation, we develop a detection criteria for samples on which a classifier is likely to fail at test time. In particular, we test against three different sources of classification failures: mistakes made on the test set due to poor model generalization, adversarial samples and out-of-distribution samples. Our approach is agnostic to class labels from the training set which makes it applicable to models trained in a semi-supervised way.
Most work on multi-document summarization has focused on generic summarization of information present in each individual document set. However, the under-explored setting of update summarization, where the goal is to identify the new information present in each set, is of equal practical interest (e.g., presenting readers with updates on an evolving news topic). In this work, we present SupMMD, a novel technique for generic and update summarization based on the maximum mean discrepancy from kernel two-sample testing. SupMMD combines both supervised learning for salience and unsupervised learning for coverage and diversity. Further, we adapt multiple kernel learning to make use of similarity across multiple information sources (e.g., text features and knowledge based concepts). We show the efficacy of SupMMD in both generic and update summarization tasks by meeting or exceeding the current state-of-the-art on the DUC-2004 and TAC-2009 datasets.
Although a vast body of literature relates to image segmentation methods that use deep neural networks (DNNs), less attention has been paid to assessing the statistical reliability of segmentation results. In this study, we interpret the segmentation results as hypotheses driven by DNN (called DNN-driven hypotheses) and propose a method by which to quantify the reliability of these hypotheses within a statistical hypothesis testing framework. Specifically, we consider a statistical hypothesis test for the difference between the object and background regions. This problem is challenging, as the difference would be falsely large because of the adaptation of the DNN to the data. To overcome this difficulty, we introduce a conditional selective inference (SI) framework -- a new statistical inference framework for data-driven hypotheses that has recently received considerable attention -- to compute exact (non-asymptotic) valid p-values for the segmentation results. To use the conditional SI framework for DNN-based segmentation, we develop a new SI algorithm based on the homotopy method, which enables us to derive the exact (non-asymptotic) sampling distribution of DNN-driven hypothesis. We conduct experiments on both synthetic and real-world datasets, through which we offer evidence that our proposed method can successfully control the false positive rate, has good performance in terms of computational efficiency, and provides good results when applied to medical image data.
Quantum machine learning models have the potential to offer speedups and better predictive accuracy compared to their classical counterparts. However, these quantum algorithms, like their classical counterparts, have been shown to also be vulnerable to input perturbations, in particular for classification problems. These can arise either from noisy implementations or, as a worst-case type of noise, adversarial attacks. In order to develop defence mechanisms and to better understand the reliability of these algorithms, it is crucial to understand their robustness properties in presence of natural noise sources or adversarial manipulation. From the observation that measurements involved in quantum classification algorithms are naturally probabilistic, we uncover and formalize a fundamental link between binary quantum hypothesis testing and provably robust quantum classification. This link leads to a tight robustness condition which puts constraints on the amount of noise a classifier can tolerate, independent of whether the noise source is natural or adversarial. Based on this result, we develop practical protocols to optimally certify robustness. Finally, since this is a robustness condition against worst-case types of noise, our result naturally extends to scenarios where the noise source is known. Thus, we also provide a framework to study the reliability of quantum classification protocols beyond the adversarial, worst-case noise scenarios.