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The two-sample problem, which consists in testing whether independent samples on $\mathbb{R}^d$ are drawn from the same (unknown) distribution, finds applications in many areas. Its study in high-dimension is the subject of much attention, especially because the information acquisition processes at work in the Big Data era often involve various sources, poorly controlled, leading to datasets possibly exhibiting a strong sampling bias. While classic methods relying on the computation of a discrepancy measure between the empirical distributions face the curse of dimensionality, we develop an alternative approach based on statistical learning and extending rank tests, capable of detecting small departures from the null assumption in the univariate case when appropriately designed. Overcoming the lack of natural order on $\mathbb{R}^d$ when $d\geq 2$, it is implemented in two steps. Assigning to each of the samples a label (positive vs. negative) and dividing them into two parts, a preorder on $\mathbb{R}^d$ defined by a real-valued scoring function is learned by means of a bipartite ranking algorithm applied to the first part and a rank test is applied next to the scores of the remaining observations to detect possible differences in distribution. Because it learns how to project the data onto the real line nearly like (any monotone transform of) the likelihood ratio between the original multivariate distributions would do, the approach is not much affected by the dimensionality, ignoring ranking model bias issues, and preserves the advantages of univariate rank tests. Nonasymptotic error bounds are proved based on recent concentration results for two-sample linear rank-processes and an experimental study shows that the approach promoted surpasses alternative methods standing as natural competitors.

The popular systemic risk measure CoVaR (conditional Value-at-Risk) is widely used in economics and finance. Formally, it is defined as an (extreme) quantile of one variable (e.g., losses in the financial system) conditional on some other variable (e.g., losses in a bank's shares) being in distress and, hence, measures the spillover of risks. In this article, we propose joint dynamic and semiparametric models for VaR and CoVaR together with a two-step M-estimator for the model parameters drawing on recently proposed bivariate scoring functions for the pair (VaR, CoVaR). Among others, this allows for the estimation of joint dynamic forecasting models for (VaR, CoVaR). We prove consistency and asymptotic normality of the proposed estimator and analyze its finite-sample properties in simulations. We apply our dynamic models to generate CoVaR forecasts for real financial data, which are shown to be superior to existing methods.

Dealing with distribution shifts is one of the central challenges for modern machine learning. One fundamental situation is the \emph{covariate shift}, where the input distributions of data change from training to testing stages while the input-conditional output distribution remains unchanged. In this paper, we initiate the study of a more challenging scenario -- \emph{continuous} covariate shift -- in which the test data appear sequentially, and their distributions can shift continuously. Our goal is to adaptively train the predictor such that its prediction risk accumulated over time can be minimized. Starting with the importance-weighted learning, we show the method works effectively if the time-varying density ratios of test and train inputs can be accurately estimated. However, existing density ratio estimation methods would fail due to data scarcity at each time step. To this end, we propose an online method that can appropriately reuse historical information. Our density ratio estimation method is proven to perform well by enjoying a dynamic regret bound, which finally leads to an excess risk guarantee for the predictor. Empirical results also validate the effectiveness.

Multiway data analysis is aimed at inferring patterns from data represented as a multi-dimensional array. Estimating covariance from multiway data is a fundamental statistical task, however, the intrinsic high dimensionality poses significant statistical and computational challenges. Recently, several factorized covariance models, paired with estimation algorithms, have been proposed to circumvent these obstacles. Despite several promising results on the algorithmic front, it remains under-explored whether and when such a model is valid. To address this question, we define the notion of Kronecker-separable multiway covariance, which can be written as a sum of $r$ tensor products of mode-wise covariances. The question of whether a given covariance can be represented as a separable multiway covariance is then reduced to an equivalent question about separability of quantum states. Using this equivalence, it follows directly that a generic multiway covariance tends to be non-separable (even if $r \to \infty$), and moreover, finding its best separable approximation is NP-hard. These observations imply that factorized covariance models are restrictive and should be used only when there is a compelling rationale for such a model.

Model fairness is an essential element for Trustworthy AI. While many techniques for model fairness have been proposed, most of them assume that the training and deployment data distributions are identical, which is often not true in practice. In particular, when the bias between labels and sensitive groups changes, the fairness of the trained model is directly influenced and can worsen. We make two contributions for solving this problem. First, we analytically show that existing in-processing fair algorithms have fundamental limits in accuracy and group fairness. We introduce the notion of correlation shifts, which can explicitly capture the change of the above bias. Second, we propose a novel pre-processing step that samples the input data to reduce correlation shifts and thus enables the in-processing approaches to overcome their limitations. We formulate an optimization problem for adjusting the data ratio among labels and sensitive groups to reflect the shifted correlation. A key benefit of our approach lies in decoupling the roles of pre- and in-processing approaches: correlation adjustment via pre-processing and unfairness mitigation on the processed data via in-processing. Experiments show that our framework effectively improves existing in-processing fair algorithms w.r.t. accuracy and fairness, both on synthetic and real datasets.

Spurious correlations, or correlations that change across domains where a model can be deployed, present significant challenges to real-world applications of machine learning models. However, such correlations are not always "spurious"; often, they provide valuable prior information for a prediction. Here, we present a test-time adaptation method that exploits the spurious correlation phenomenon, in contrast to recent approaches that attempt to eliminate spurious correlations through invariance. We consider situations where the prior distribution $p(y, z)$, which models the dependence between the class label $y$ and the "nuisance" factors $z$, may change across domains, but the generative model for features $p(\mathbf{x}|y, z)$ is constant. We note that this corresponds to an expanded version of the label shift assumption, where the labels now also include the nuisance factors $z$. Based on this observation, we train a classifier to predict $p(y, z|\mathbf{x})$ on the source distribution, and propose a test-time label shift correction that adapts to changes in the marginal distribution $p(y, z)$ using unlabeled samples from the target domain. We evaluate our method, which we call "Test-Time Label-Shift Adaptation" (TTLSA), on two different image datasets -- the CheXpert chest X-ray dataset and the Colored MNIST dataset -- and show a significant improvement over baseline methods. Code reproducing experiments is available at //github.com/nalzok/test-time-label-shift .

Unsupervised domain adaptation has recently emerged as an effective paradigm for generalizing deep neural networks to new target domains. However, there is still enormous potential to be tapped to reach the fully supervised performance. In this paper, we present a novel active learning strategy to assist knowledge transfer in the target domain, dubbed active domain adaptation. We start from an observation that energy-based models exhibit free energy biases when training (source) and test (target) data come from different distributions. Inspired by this inherent mechanism, we empirically reveal that a simple yet efficient energy-based sampling strategy sheds light on selecting the most valuable target samples than existing approaches requiring particular architectures or computation of the distances. Our algorithm, Energy-based Active Domain Adaptation (EADA), queries groups of targe data that incorporate both domain characteristic and instance uncertainty into every selection round. Meanwhile, by aligning the free energy of target data compact around the source domain via a regularization term, domain gap can be implicitly diminished. Through extensive experiments, we show that EADA surpasses state-of-the-art methods on well-known challenging benchmarks with substantial improvements, making it a useful option in the open world. Code is available at //github.com/BIT-DA/EADA.

The dominating NLP paradigm of training a strong neural predictor to perform one task on a specific dataset has led to state-of-the-art performance in a variety of applications (eg. sentiment classification, span-prediction based question answering or machine translation). However, it builds upon the assumption that the data distribution is stationary, ie. that the data is sampled from a fixed distribution both at training and test time. This way of training is inconsistent with how we as humans are able to learn from and operate within a constantly changing stream of information. Moreover, it is ill-adapted to real-world use cases where the data distribution is expected to shift over the course of a model's lifetime. The first goal of this thesis is to characterize the different forms this shift can take in the context of natural language processing, and propose benchmarks and evaluation metrics to measure its effect on current deep learning architectures. We then proceed to take steps to mitigate the effect of distributional shift on NLP models. To this end, we develop methods based on parametric reformulations of the distributionally robust optimization framework. Empirically, we demonstrate that these approaches yield more robust models as demonstrated on a selection of realistic problems. In the third and final part of this thesis, we explore ways of efficiently adapting existing models to new domains or tasks. Our contribution to this topic takes inspiration from information geometry to derive a new gradient update rule which alleviate catastrophic forgetting issues during adaptation.

Clustering is one of the most fundamental and wide-spread techniques in exploratory data analysis. Yet, the basic approach to clustering has not really changed: a practitioner hand-picks a task-specific clustering loss to optimize and fit the given data to reveal the underlying cluster structure. Some types of losses---such as k-means, or its non-linear version: kernelized k-means (centroid based), and DBSCAN (density based)---are popular choices due to their good empirical performance on a range of applications. Although every so often the clustering output using these standard losses fails to reveal the underlying structure, and the practitioner has to custom-design their own variation. In this work we take an intrinsically different approach to clustering: rather than fitting a dataset to a specific clustering loss, we train a recurrent model that learns how to cluster. The model uses as training pairs examples of datasets (as input) and its corresponding cluster identities (as output). By providing multiple types of training datasets as inputs, our model has the ability to generalize well on unseen datasets (new clustering tasks). Our experiments reveal that by training on simple synthetically generated datasets or on existing real datasets, we can achieve better clustering performance on unseen real-world datasets when compared with standard benchmark clustering techniques. Our meta clustering model works well even for small datasets where the usual deep learning models tend to perform worse.

Many tasks in natural language processing can be viewed as multi-label classification problems. However, most of the existing models are trained with the standard cross-entropy loss function and use a fixed prediction policy (e.g., a threshold of 0.5) for all the labels, which completely ignores the complexity and dependencies among different labels. In this paper, we propose a meta-learning method to capture these complex label dependencies. More specifically, our method utilizes a meta-learner to jointly learn the training policies and prediction policies for different labels. The training policies are then used to train the classifier with the cross-entropy loss function, and the prediction policies are further implemented for prediction. Experimental results on fine-grained entity typing and text classification demonstrate that our proposed method can obtain more accurate multi-label classification results.