We propose a novel semi-parametric classifier based on Mahalanobis distances of an observation from the competing classes. Our tool is a generalized additive model with the logistic link function that uses these distances as features to estimate the posterior probabilities of the different classes. While popular parametric classifiers like linear and quadratic discriminant analyses are mainly motivated by the normality of the underlying distributions, the proposed classifier is more flexible and free from such parametric assumptions. Since the densities of elliptic distributions are functions of Mahalanobis distances, this classifier works well when the competing classes are (nearly) elliptic. In such cases, it often outperforms popular nonparametric classifiers, especially when the sample size is small compared to the dimension of the data. To cope with non-elliptic and possibly multimodal distributions, we propose a local version of the Mahalanobis distance. Subsequently, we propose another classifier based on a generalized additive model that uses the local Mahalanobis distances as features. This nonparametric classifier usually performs like the Mahalanobis distance based semiparametric classifier when the underlying distributions are elliptic, but outperforms it for several non-elliptic and multimodal distributions. We also investigate the behaviour of these two classifiers in high dimension, low sample size situations. A thorough numerical study involving several simulated and real datasets demonstrate the usefulness of the proposed classifiers in comparison to many state-of-the-art methods.
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We propose a novel test-time optimization approach for efficiently and robustly tracking any pixel at any time in a video. The latest state-of-the-art optimization-based tracking technique, OmniMotion, requires a prohibitively long optimization time, rendering it impractical for downstream applications. OmniMotion is sensitive to the choice of random seeds, leading to unstable convergence. To improve efficiency and robustness, we introduce a novel invertible deformation network, CaDeX++, which factorizes the function representation into a local spatial-temporal feature grid and enhances the expressivity of the coupling blocks with non-linear functions. While CaDeX++ incorporates a stronger geometric bias within its architectural design, it also takes advantage of the inductive bias provided by the vision foundation models. Our system utilizes monocular depth estimation to represent scene geometry and enhances the objective by incorporating DINOv2 long-term semantics to regulate the optimization process. Our experiments demonstrate a substantial improvement in training speed (more than \textbf{10 times} faster), robustness, and accuracy in tracking over the SoTA optimization-based method OmniMotion.
Uniform preorders are a class of combinatory representations of Set-indexed preorders that generalize Pieter Hofstra's basic relational objects. An indexed preorder is representable by a uniform preorder if and only if it has as generic predicate. We study the $\exists$-completion of indexed preorders on the level of uniform preorders, and identify a combinatory condition (called 'relational completeness') which characterizes those uniform preorders with finite meets whose $\exists$-completions are triposes. The class of triposes obtained this way contains relative realizability triposes, for which we derive a characterization as a fibrational analogue of the characterization of realizability toposes given in earlier work. Besides relative partial combinatory algebras, the class of relationally complete uniform preorders contains filtered ordered partial combinatory algebras, and it is unclear if there are any others.
This paper studies Ebert's hat problem for three and four players and two colors, where the probabilities of the colors may be different for each player. Our goal is to maximize the probability of winning the game and to describe winning strategies We use the concept of an adequate set. The construction of adequate sets is independent of underlying probabilities and we can use this fact in the analysis of our general case.
Observations of groundwater pollutants, such as arsenic or Perfluorooctane sulfonate (PFOS), are riddled with left censoring. These measurements have impact on the health and lifestyle of the populace. Left censoring of these spatially correlated observations are usually addressed by applying Gaussian processes (GPs), which have theoretical advantages. However, this comes with a challenging computational complexity of $\mathcal{O}(n^3)$, which is impractical for large datasets. Additionally, a sizable proportion of the data being left-censored creates further bottlenecks, since the likelihood computation now involves an intractable high-dimensional integral of the multivariate Gaussian density. In this article, we tackle these two problems simultaneously by approximating the GP with a Gaussian Markov random field (GMRF) approach that exploits an explicit link between a GP with Mat\'ern correlation function and a GMRF using stochastic partial differential equations (SPDEs). We introduce a GMRF-based measurement error into the model, which alleviates the likelihood computation for the censored data, drastically improving the speed of the model while maintaining admirable accuracy. Our approach demonstrates robustness and substantial computational scalability, compared to state-of-the-art methods for censored spatial responses across various simulation settings. Finally, the fit of this fully Bayesian model to the concentration of PFOS in groundwater available at 24,959 sites across California, where 46.62\% responses are censored, produces prediction surface and uncertainty quantification in real time, thereby substantiating the applicability and scalability of the proposed method. Code for implementation is made available via GitHub.
Watermarking approaches are proposed to identify if text being circulated is human or large language model (LLM) generated. The state-of-the-art watermarking strategy of Kirchenbauer et al. (2023a) biases the LLM to generate specific (``green'') tokens. However, determining the robustness of this watermarking method is an open problem. Existing attack methods fail to evade detection for longer text segments. We overcome this limitation, and propose {\em Self Color Testing-based Substitution (SCTS)}, the first ``color-aware'' attack. SCTS obtains color information by strategically prompting the watermarked LLM and comparing output tokens frequencies. It uses this information to determine token colors, and substitutes green tokens with non-green ones. In our experiments, SCTS successfully evades watermark detection using fewer number of edits than related work. Additionally, we show both theoretically and empirically that SCTS can remove the watermark for arbitrarily long watermarked text.
Graph Convolutional Network (GCN) has achieved extraordinary success in learning effective task-specific representations of nodes in graphs. However, regarding Heterogeneous Information Network (HIN), existing HIN-oriented GCN methods still suffer from two deficiencies: (1) they cannot flexibly explore all possible meta-paths and extract the most useful ones for a target object, which hinders both effectiveness and interpretability; (2) they often need to generate intermediate meta-path based dense graphs, which leads to high computational complexity. To address the above issues, we propose an interpretable and efficient Heterogeneous Graph Convolutional Network (ie-HGCN) to learn the representations of objects in HINs. It is designed as a hierarchical aggregation architecture, i.e., object-level aggregation first, followed by type-level aggregation. The novel architecture can automatically extract useful meta-paths for each object from all possible meta-paths (within a length limit), which brings good model interpretability. It can also reduce the computational cost by avoiding intermediate HIN transformation and neighborhood attention. We provide theoretical analysis about the proposed ie-HGCN in terms of evaluating the usefulness of all possible meta-paths, its connection to the spectral graph convolution on HINs, and its quasi-linear time complexity. Extensive experiments on three real network datasets demonstrate the superiority of ie-HGCN over the state-of-the-art methods.
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.
Modern neural network training relies heavily on data augmentation for improved generalization. After the initial success of label-preserving augmentations, there has been a recent surge of interest in label-perturbing approaches, which combine features and labels across training samples to smooth the learned decision surface. In this paper, we propose a new augmentation method that leverages the first and second moments extracted and re-injected by feature normalization. We replace the moments of the learned features of one training image by those of another, and also interpolate the target labels. As our approach is fast, operates entirely in feature space, and mixes different signals than prior methods, one can effectively combine it with existing augmentation methods. We demonstrate its efficacy across benchmark data sets in computer vision, speech, and natural language processing, where it consistently improves the generalization performance of highly competitive baseline networks.
Aspect level sentiment classification aims to identify the sentiment expressed towards an aspect given a context sentence. Previous neural network based methods largely ignore the syntax structure in one sentence. In this paper, we propose a novel target-dependent graph attention network (TD-GAT) for aspect level sentiment classification, which explicitly utilizes the dependency relationship among words. Using the dependency graph, it propagates sentiment features directly from the syntactic context of an aspect target. In our experiments, we show our method outperforms multiple baselines with GloVe embeddings. We also demonstrate that using BERT representations further substantially boosts the performance.
We study the problem of textual relation embedding with distant supervision. To combat the wrong labeling problem of distant supervision, we propose to embed textual relations with global statistics of relations, i.e., the co-occurrence statistics of textual and knowledge base relations collected from the entire corpus. This approach turns out to be more robust to the training noise introduced by distant supervision. On a popular relation extraction dataset, we show that the learned textual relation embedding can be used to augment existing relation extraction models and significantly improve their performance. Most remarkably, for the top 1,000 relational facts discovered by the best existing model, the precision can be improved from 83.9% to 89.3%.
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