Many modern datasets are collected automatically and are thus easily contaminated by outliers. This led to a regain of interest in robust estimation, including new notions of robustness such as robustness to adversarial contamination of the data. However, most robust estimation methods are designed for a specific model. Notably, many methods were proposed recently to obtain robust estimators in linear models (or generalized linear models), and a few were developed for very specific settings, for example beta regression or sample selection models. In this paper we develop a new approach for robust estimation in arbitrary regression models, based on Maximum Mean Discrepancy minimization. We build two estimators which are both proven to be robust to Huber-type contamination. We obtain a non-asymptotic error bound for one them and show that it is also robust to adversarial contamination, but this estimator is computationally more expensive to use in practice than the other one. As a by-product of our theoretical analysis of the proposed estimators we derive new results on kernel conditional mean embedding of distributions which are of independent interest.
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In conventional supervised classification, true labels are required for individual instances. However, it could be prohibitive to collect the true labels for individual instances, due to privacy concerns or unaffordable annotation costs. This motivates the study on classification from aggregate observations (CFAO), where the supervision is provided to groups of instances, instead of individual instances. CFAO is a generalized learning framework that contains various learning problems, such as multiple-instance learning and learning from label proportions. The goal of this paper is to present a novel universal method of CFAO, which holds an unbiased estimator of the classification risk for arbitrary losses -- previous research failed to achieve this goal. Practically, our method works by weighing the importance of each label for each instance in the group, which provides purified supervision for the classifier to learn. Theoretically, our proposed method not only guarantees the risk consistency due to the unbiased risk estimator but also can be compatible with arbitrary losses. Extensive experiments on various problems of CFAO demonstrate the superiority of our proposed method.
Segmentation-based methods have achieved great success for arbitrary shape text detection. However, separating neighboring text instances is still one of the most challenging problems due to the complexity of texts in scene images. In this paper, we propose an innovative Kernel Proposal Network (dubbed KPN) for arbitrary shape text detection. The proposed KPN can separate neighboring text instances by classifying different texts into instance-independent feature maps, meanwhile avoiding the complex aggregation process existing in segmentation-based arbitrary shape text detection methods. To be concrete, our KPN will predict a Gaussian center map for each text image, which will be used to extract a series of candidate kernel proposals (i.e., dynamic convolution kernel) from the embedding feature maps according to their corresponding keypoint positions. To enforce the independence between kernel proposals, we propose a novel orthogonal learning loss (OLL) via orthogonal constraints. Specifically, our kernel proposals contain important self-information learned by network and location information by position embedding. Finally, kernel proposals will individually convolve all embedding feature maps for generating individual embedded maps of text instances. In this way, our KPN can effectively separate neighboring text instances and improve the robustness against unclear boundaries. To our knowledge, our work is the first to introduce the dynamic convolution kernel strategy to efficiently and effectively tackle the adhesion problem of neighboring text instances in text detection. Experimental results on challenging datasets verify the impressive performance and efficiency of our method. The code and model are available at //github.com/GXYM/KPN.
The principle of maximum entropy, as introduced by Jaynes in information theory, has contributed to advancements in various domains such as Statistical Mechanics, Machine Learning, and Ecology. Its resultant solutions have served as a catalyst, facilitating researchers in mapping their empirical observations to the acquisition of unbiased models, whilst deepening the understanding of complex systems and phenomena. However, when we consider situations in which the model elements are not directly observable, such as when noise or ocular occlusion is present, possibilities arise for which standard maximum entropy approaches may fail, as they are unable to match feature constraints. Here we show the Principle of Uncertain Maximum Entropy as a method that both encodes all available information in spite of arbitrarily noisy observations while surpassing the accuracy of some ad-hoc methods. Additionally, we utilize the output of a black-box machine learning model as input into an uncertain maximum entropy model, resulting in a novel approach for scenarios where the observation function is unavailable. Previous remedies either relaxed feature constraints when accounting for observation error, given well-characterized errors such as zero-mean Gaussian, or chose to simply select the most likely model element given an observation. We anticipate our principle finding broad applications in diverse fields due to generalizing the traditional maximum entropy method with the ability to utilize uncertain observations.
In this article, we introduce a new parameterized family of topological invariants, taking the form of candidate decompositions, for multi-parameter persistence modules. We prove that our candidate decompositions are controllable approximations: when restricting to modules that can be decomposed into interval summands, we establish theoretical results about the approximation error between our candidate decompositions and the true underlying module in terms of the standard interleaving and bottleneck distances. Moreover, even when the underlying module does not admit such a decomposition, our candidate decompositions are nonetheless stable invariants; small perturbations in the underlying module lead to small perturbations in the candidate decomposition. Then, we introduce MMA (Multipersistence Module Approximation): an algorithm for computing stable instances of such invariants, which is based on fibered barcodes and exact matchings, two constructions that stem from the theory of single-parameter persistence. By design, MMA can handle an arbitrary number of filtrations, and has bounded complexity and running time. Finally, we present empirical evidence validating the generalization capabilities and running time speed-ups of MMA on several data sets.
A fundamental problem in data management is to find the elements in an array that match a query. Recently, learned indexes are being extensively used to solve this problem, where they learn a model to predict the location of the items in the array. They are empirically shown to outperform non-learned methods (e.g., B-trees or binary search that answer queries in $O(\log n)$ time) by orders of magnitude. However, success of learned indexes has not been theoretically justified. Only existing attempt shows the same query time of $O(\log n)$, but with a constant factor improvement in space complexity over non-learned methods, under some assumptions on data distribution. In this paper, we significantly strengthen this result, showing that under mild assumptions on data distribution, and the same space complexity as non-learned methods, learned indexes can answer queries in $O(\log\log n)$ expected query time. We also show that allowing for slightly larger but still near-linear space overhead, a learned index can achieve $O(1)$ expected query time. Our results theoretically prove learned indexes are orders of magnitude faster than non-learned methods, theoretically grounding their empirical success.
We study optimization methods to train local (or personalized) models for decentralized collections of local datasets with an intrinsic network structure. This network structure arises from domain-specific notions of similarity between local datasets. Examples for such notions include spatio-temporal proximity, statistical dependencies or functional relations. Our main conceptual contribution is to formulate federated learning as generalized total variation (GTV) minimization. This formulation unifies and considerably extends existing federated learning methods. It is highly flexible and can be combined with a broad range of parametric models, including generalized linear models or deep neural networks. Our main algorithmic contribution is a fully decentralized federated learning algorithm. This algorithm is obtained by applying an established primal-dual method to solve GTV minimization. It can be implemented as message passing and is robust against inexact computations that arise from limited computational resources including processing time or bandwidth. Our main analytic contribution is an upper bound on the deviation between the local model parameters learnt by our algorithm and an oracle-based clustered federated learning method. This upper bound reveals conditions on the local models and the network structure of local datasets such that GTV minimization is able to pool (nearly) homogeneous local datasets.
Based on binary inquiries, we developed an algorithm to estimate population quantiles under Local Differential Privacy (LDP). By self-normalizing, our algorithm provides asymptotically normal estimation with valid inference, resulting in tight confidence intervals without the need for nuisance parameters to be estimated. Our proposed method can be conducted fully online, leading to high computational efficiency and minimal storage requirements with $\mathcal{O}(1)$ space. We also proved an optimality result by an elegant application of one central limit theorem of Gaussian Differential Privacy (GDP) when targeting the frequently encountered median estimation problem. With mathematical proof and extensive numerical testing, we demonstrate the validity of our algorithm both theoretically and experimentally.
We investigate how to improve efficiency using regression adjustments with covariates in covariate-adaptive randomizations (CARs) with imperfect subject compliance. Our regression-adjusted estimators, which are based on the doubly robust moment for local average treatment effects, are consistent and asymptotically normal even with heterogeneous probability of assignment and misspecified regression adjustments. We propose an optimal but potentially misspecified linear adjustment and its further improvement via a nonlinear adjustment, both of which lead to more efficient estimators than the one without adjustments. We also provide conditions for nonparametric and regularized adjustments to achieve the semiparametric efficiency bound under CARs.
We consider the multiple testing of the general regression framework aiming at studying the relationship between a univariate response and a p-dimensional predictor. To test the hypothesis of the effect of each predictor, we construct an Angular Balanced Statistic (ABS) based on the estimator of the sliced inverse regression without assuming a model of the conditional distribution of the response. According to the developed limiting distribution results in this paper, we have shown that ABS is asymptotically symmetric with respect to zero under the null hypothesis. We then propose a Model-free multiple Testing procedure using Angular balanced statistics (MTA) and show theoretically that the false discovery rate of this method is less than or equal to a designated level asymptotically. Numerical evidence has shown that the MTA method is much more powerful than its alternatives, subject to the control of the false discovery rate.
Multivariate sequential data collected in practice often exhibit temporal irregularities, including nonuniform time intervals and component misalignment. However, if uneven spacing and asynchrony are endogenous characteristics of the data rather than a result of insufficient observation, the information content of these irregularities plays a defining role in characterizing the multivariate dependence structure. Existing approaches for probabilistic forecasting either overlook the resulting statistical heterogeneities, are susceptible to imputation biases, or impose parametric assumptions on the data distribution. This paper proposes an end-to-end solution that overcomes these limitations by allowing the observation arrival times to play the central role of model construction, which is at the core of temporal irregularities. To acknowledge temporal irregularities, we first enable unique hidden states for components so that the arrival times can dictate when, how, and which hidden states to update. We then develop a conditional flow representation to non-parametrically represent the data distribution, which is typically non-Gaussian, and supervise this representation by carefully factorizing the log-likelihood objective to select conditional information that facilitates capturing time variation and path dependency. The broad applicability and superiority of the proposed solution are confirmed by comparing it with existing approaches through ablation studies and testing on real-world datasets.
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