We study the problem of recovering Gaussian data under adversarial corruptions when the noises are low-rank and the corruptions are on the coordinate level. Concretely, we assume that the Gaussian noises lie in an unknown $k$-dimensional subspace $U \subseteq \mathbb{R}^d$, and $s$ randomly chosen coordinates of each data point fall into the control of an adversary. This setting models the scenario of learning from high-dimensional yet structured data that are transmitted through a highly-noisy channel, so that the data points are unlikely to be entirely clean. Our main result is an efficient algorithm that, when $ks^2 = O(d)$, recovers every single data point up to a nearly-optimal $\ell_1$ error of $\tilde O(ks/d)$ in expectation. At the core of our proof is a new analysis of the well-known Basis Pursuit (BP) method for recovering a sparse signal, which is known to succeed under additional assumptions (e.g., incoherence or the restricted isometry property) on the underlying subspace $U$. In contrast, we present a novel approach via studying a natural combinatorial problem and show that, over the randomness in the support of the sparse signal, a high-probability error bound is possible even if the subspace $U$ is arbitrary.
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This paper considers the optimal sensor allocation for estimating the emission rates of multiple sources in a two-dimensional spatial domain. Locations of potential emission sources are known (e.g., factory stacks), and the number of sources is much greater than the number of sensors that can be deployed, giving rise to the optimal sensor allocation problem. In particular, we consider linear dispersion forward models, and the optimal sensor allocation is formulated as a bilevel optimization problem. The outer problem determines the optimal sensor locations by minimizing the overall Mean Squared Error of the estimated emission rates over various wind conditions, while the inner problem solves an inverse problem that estimates the emission rates. Two algorithms, including the repeated Sample Average Approximation and the Stochastic Gradient Descent based bilevel approximation, are investigated in solving the sensor allocation problem. Convergence analysis is performed to obtain the performance guarantee, and numerical examples are presented to illustrate the proposed approach.
We investigate two possible techniques to authenticate the q-digest data structure, along with a worst-case study of the computational complexity both in time and space of the proposed solutions, and considerations on the feasibility of the presented approaches in real-world scenarios. We conclude the discussion by presenting some considerations on the information complexity of the queries in the two proposed approaches, and by presenting some interesting ideas that could be the subject of future studies on the topic.
We propose an adjusted Wasserstein distributionally robust estimator -- based on a nonlinear transformation of the Wasserstein distributionally robust (WDRO) estimator in statistical learning. The classic WDRO estimator is asymptotically biased, while our adjusted WDRO estimator is asymptotically unbiased, resulting in a smaller asymptotic mean squared error. Meanwhile, the proposed adjusted WDRO has an out-of-sample performance guarantee. Further, under certain conditions, our proposed adjustment technique provides a general principle to de-bias asymptotically biased estimators. Specifically, we will investigate how the adjusted WDRO estimator is developed in the generalized linear model, including logistic regression, linear regression, and Poisson regression. Numerical experiments demonstrate the favorable practical performance of the adjusted estimator over the classic one.
In online multiple testing, an a priori unknown number of hypotheses are tested sequentially, i.e. at each time point a test decision for the current hypothesis has to be made using only the data available so far. Although many powerful test procedures have been developed for online error control in recent years, most of them are designed solely for independent or at most locally dependent test statistics. In this work, we provide a new framework for deriving online multiple test procedures which ensure asymptotical (with respect to the sample size) control of the familywise error rate (FWER), regardless of the dependence structure between test statistics. In this context, we give a few concrete examples of such test procedures and discuss their properties. Furthermore, we conduct a simulation study in which the type I error control of these test procedures is also confirmed for a finite sample size and a gain in power is indicated.
Recommender systems often grapple with noisy implicit feedback. Most studies alleviate the noise issues from data cleaning perspective such as data resampling and reweighting, but they are constrained by heuristic assumptions. Another denoising avenue is from model perspective, which proactively injects noises into user-item interactions and enhance the intrinsic denoising ability of models. However, this kind of denoising process poses significant challenges to the recommender model's representation capacity to capture noise patterns. To address this issue, we propose Denoising Diffusion Recommender Model (DDRM), which leverages multi-step denoising process based on diffusion models to robustify user and item embeddings from any recommender models. DDRM injects controlled Gaussian noises in the forward process and iteratively removes noises in the reverse denoising process, thereby improving embedding robustness against noisy feedback. To achieve this target, the key lies in offering appropriate guidance to steer the reverse denoising process and providing a proper starting point to start the forward-reverse process during inference. In particular, we propose a dedicated denoising module that encodes collaborative information as denoising guidance. Besides, in the inference stage, DDRM utilizes the average embeddings of users' historically liked items as the starting point rather than using pure noise since pure noise lacks personalization, which increases the difficulty of the denoising process. Extensive experiments on three datasets with three representative backend recommender models demonstrate the effectiveness of DDRM.
Recent contrastive representation learning methods rely on estimating mutual information (MI) between multiple views of an underlying context. E.g., we can derive multiple views of a given image by applying data augmentation, or we can split a sequence into views comprising the past and future of some step in the sequence. Contrastive lower bounds on MI are easy to optimize, but have a strong underestimation bias when estimating large amounts of MI. We propose decomposing the full MI estimation problem into a sum of smaller estimation problems by splitting one of the views into progressively more informed subviews and by applying the chain rule on MI between the decomposed views. This expression contains a sum of unconditional and conditional MI terms, each measuring modest chunks of the total MI, which facilitates approximation via contrastive bounds. To maximize the sum, we formulate a contrastive lower bound on the conditional MI which can be approximated efficiently. We refer to our general approach as Decomposed Estimation of Mutual Information (DEMI). We show that DEMI can capture a larger amount of MI than standard non-decomposed contrastive bounds in a synthetic setting, and learns better representations in a vision domain and for dialogue generation.
Transformers have become one of the most important architectural innovations in deep learning and have enabled many breakthroughs over the past few years. Here we propose a simple attention-free network architecture, gMLP, based solely on MLPs with gating, and show that it can perform as well as Transformers in key language and vision applications. Our comparisons show that self-attention is not critical for Vision Transformers, as gMLP can achieve the same accuracy. For BERT, our model achieves parity with Transformers on pretraining perplexity and is better on some downstream tasks. On finetuning tasks where gMLP performs worse, making the gMLP model substantially larger can close the gap with Transformers. In general, our experiments show that gMLP can scale as well as Transformers over increased data and compute.
Graphical causal inference as pioneered by Judea Pearl arose from research on artificial intelligence (AI), and for a long time had little connection to the field of machine learning. This article discusses where links have been and should be established, introducing key concepts along the way. It argues that the hard open problems of machine learning and AI are intrinsically related to causality, and explains how the field is beginning to understand them.
The present paper surveys neural approaches to conversational AI that have been developed in the last few years. We group conversational systems into three categories: (1) question answering agents, (2) task-oriented dialogue agents, and (3) chatbots. For each category, we present a review of state-of-the-art neural approaches, draw the connection between them and traditional approaches, and discuss the progress that has been made and challenges still being faced, using specific systems and models as case studies.
Multi-relation Question Answering is a challenging task, due to the requirement of elaborated analysis on questions and reasoning over multiple fact triples in knowledge base. In this paper, we present a novel model called Interpretable Reasoning Network that employs an interpretable, hop-by-hop reasoning process for question answering. The model dynamically decides which part of an input question should be analyzed at each hop; predicts a relation that corresponds to the current parsed results; utilizes the predicted relation to update the question representation and the state of the reasoning process; and then drives the next-hop reasoning. Experiments show that our model yields state-of-the-art results on two datasets. More interestingly, the model can offer traceable and observable intermediate predictions for reasoning analysis and failure diagnosis.
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