Developing simple, sample-efficient learning algorithms for robust classification is a pressing issue in today's tech-dominated world, and current theoretical techniques requiring exponential sample complexity and complicated improper learning rules fall far from answering the need. In this work we study the fundamental paradigm of (robust) $\textit{empirical risk minimization}$ (RERM), a simple process in which the learner outputs any hypothesis minimizing its training error. RERM famously fails to robustly learn VC classes (Montasser et al., 2019a), a bound we show extends even to `nice' settings such as (bounded) halfspaces. As such, we study a recent relaxation of the robust model called $\textit{tolerant}$ robust learning (Ashtiani et al., 2022) where the output classifier is compared to the best achievable error over slightly larger perturbation sets. We show that under geometric niceness conditions, a natural tolerant variant of RERM is indeed sufficient for $\gamma$-tolerant robust learning VC classes over $\mathbb{R}^d$, and requires only $\tilde{O}\left( \frac{VC(H)d\log \frac{D}{\gamma\delta}}{\epsilon^2}\right)$ samples for robustness regions of (maximum) diameter $D$.
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Developing gaze estimation models that generalize well to unseen domains and in-the-wild conditions remains a challenge with no known best solution. This is mostly due to the difficulty of acquiring ground truth data that cover the distribution of possible faces, head poses and environmental conditions that exist in the real world. In this work, we propose to train general gaze estimation models based on 3D geometry-aware gaze pseudo-annotations which we extract from arbitrary unlabelled face images, which are abundantly available in the internet. Additionally, we leverage the observation that head, body and hand pose estimation benefit from revising them as dense 3D coordinate prediction, and similarly express gaze estimation as regression of dense 3D eye meshes. We overcome the absence of compatible ground truth by fitting rigid 3D eyeballs on existing gaze datasets and design a multi-view supervision framework to balance the effect of pseudo-labels during training. We test our method in the task of gaze generalization, in which we demonstrate improvement of up to $30\%$ compared to state-of-the-art when no ground truth data are available, and up to $10\%$ when they are. The project material will become available for research purposes.
Stochastic gradient descent (SGD) is a scalable and memory-efficient optimization algorithm for large datasets and stream data, which has drawn a great deal of attention and popularity. The applications of SGD-based estimators to statistical inference such as interval estimation have also achieved great success. However, most of the related works are based on i.i.d. observations or Markov chains. When the observations come from a mixing time series, how to conduct valid statistical inference remains unexplored. As a matter of fact, the general correlation among observations imposes a challenge on interval estimation. Most existing methods may ignore this correlation and lead to invalid confidence intervals. In this paper, we propose a mini-batch SGD estimator for statistical inference when the data is $\phi$-mixing. The confidence intervals are constructed using an associated mini-batch bootstrap SGD procedure. Using ``independent block'' trick from \cite{yu1994rates}, we show that the proposed estimator is asymptotically normal, and its limiting distribution can be effectively approximated by the bootstrap procedure. The proposed method is memory-efficient and easy to implement in practice. Simulation studies on synthetic data and an application to a real-world dataset confirm our theory.
Dictionary learning, the problem of recovering a sparsely used matrix $\mathbf{D} \in \mathbb{R}^{M \times K}$ and $N$ $s$-sparse vectors $\mathbf{x}_i \in \mathbb{R}^{K}$ from samples of the form $\mathbf{y}_i = \mathbf{D}\mathbf{x}_i$, is of increasing importance to applications in signal processing and data science. When the dictionary is known, recovery of $\mathbf{x}_i$ is possible even for sparsity linear in dimension $M$, yet to date, the only algorithms which provably succeed in the linear sparsity regime are Riemannian trust-region methods, which are limited to orthogonal dictionaries, and methods based on the sum-of-squares hierarchy, which requires super-polynomial time in order to obtain an error which decays in $M$. In this work, we introduce SPORADIC (SPectral ORAcle DICtionary Learning), an efficient spectral method on family of reweighted covariance matrices. We prove that in high enough dimensions, SPORADIC can recover overcomplete ($K > M$) dictionaries satisfying the well-known restricted isometry property (RIP) even when sparsity is linear in dimension up to logarithmic factors. Moreover, these accuracy guarantees have an ``oracle property" that the support and signs of the unknown sparse vectors $\mathbf{x}_i$ can be recovered exactly with high probability, allowing for arbitrarily close estimation of $\mathbf{D}$ with enough samples in polynomial time. To the author's knowledge, SPORADIC is the first polynomial-time algorithm which provably enjoys such convergence guarantees for overcomplete RIP matrices in the near-linear sparsity regime.
As a predictor's quality is often assessed by means of its risk, it is natural to regard risk consistency as a desirable property of learning methods, and many such methods have indeed been shown to be risk consistent. The first aim of this paper is to establish the close connection between risk consistency and $L_p$-consistency for a considerably wider class of loss functions than has been done before. The attempt to transfer this connection to shifted loss functions surprisingly reveals that this shift does not reduce the assumptions needed on the underlying probability measure to the same extent as it does for many other results. The results are applied to regularized kernel methods such as support vector machines.
We propose a simple and application-friendly network (called SimpleNet) for detecting and localizing anomalies. SimpleNet consists of four components: (1) a pre-trained Feature Extractor that generates local features, (2) a shallow Feature Adapter that transfo local features towards target domain, (3) a simple Anomaly Feature Generator that counterfeits anomaly features by adding Gaussian noise to normal features, and (4) a binary Anomaly Discriminator that distinguishes anomaly features from normal features. During inference, the Anomaly Feature Generator would be discarded. Our approach is based on three intuitions. First, transforming pre-trained features to target-oriented features helps avoid domain bias. Second, generating synthetic anomalies in feature space is more effective, as defects may not have much commonality in the image space. Third, a simple discriminator is much efficient and practical. In spite of simplicity, SimpleNet outperforms previous methods quantitatively and qualitatively. On the MVTec AD benchmark, SimpleNet achieves an anomaly detection AUROC of 99.6%, reducing the error by 55.5% compared to the next best performing model. Furthermore, SimpleNet is faster than existing methods, with a high frame rate of 77 FPS on a 3080ti GPU. Additionally, SimpleNet demonstrates significant improvements in performance on the One-Class Novelty Detection task. Code: //github.com/DonaldRR/SimpleNet.
Face parsing is defined as the per-pixel labeling of images containing human faces. The labels are defined to identify key facial regions like eyes, lips, nose, hair, etc. In this work, we make use of the structural consistency of the human face to propose a lightweight face-parsing method using a Local Implicit Function network, FP-LIIF. We propose a simple architecture having a convolutional encoder and a pixel MLP decoder that uses 1/26th number of parameters compared to the state-of-the-art models and yet matches or outperforms state-of-the-art models on multiple datasets, like CelebAMask-HQ and LaPa. We do not use any pretraining, and compared to other works, our network can also generate segmentation at different resolutions without any changes in the input resolution. This work enables the use of facial segmentation on low-compute or low-bandwidth devices because of its higher FPS and smaller model size.
We present a study of a kernel-based two-sample test statistic related to the Maximum Mean Discrepancy (MMD) in the manifold data setting, assuming that high-dimensional observations are close to a low-dimensional manifold. We characterize the test level and power in relation to the kernel bandwidth, the number of samples, and the intrinsic dimensionality of the manifold. Specifically, we show that when data densities are supported on a $d$-dimensional sub-manifold $\mathcal{M}$ embedded in an $m$-dimensional space, the kernel two-sample test for data sampled from a pair of distributions $p$ and $q$ that are H\"older with order $\beta$ (up to 2) is powerful when the number of samples $n$ is large such that $\Delta_2 \gtrsim n^{- { 2 \beta/( d + 4 \beta ) }}$, where $\Delta_2$ is the squared $L^2$-divergence between $p$ and $q$ on manifold. We establish a lower bound on the test power for finite $n$ that is sufficiently large, where the kernel bandwidth parameter $\gamma$ scales as $n^{-1/(d+4\beta)}$. The analysis extends to cases where the manifold has a boundary, and the data samples contain high-dimensional additive noise. Our results indicate that the kernel two-sample test does not have a curse-of-dimensionality when the data lie on or near a low-dimensional manifold. We validate our theory and the properties of the kernel test for manifold data through a series of numerical experiments.
The maximum depth estimator (aka depth median) ($\bs{\beta}^*_{RD}$) induced from regression depth (RD) of Rousseeuw and Hubert (1999) (RH99) is one of the most prevailing estimators in regression. It possesses outstanding robustness similar to the univariate location counterpart. Indeed, $\bs{\beta}^*_{RD}$ can, asymptotically, resist up to $33\%$ contamination without breakdown, in contrast to the $0\%$ for the traditional (least squares and least absolute deviations) estimators (see Van Aelst and Rousseeuw, 2000) (VAR00)). The results from VAR00 are pioneering, yet they are limited to regression-symmetric populations (with a strictly positive density) and the $\epsilon$-contamination and maximum-bias model. With a fixed finite-sample size practice, the most prevailing measure of robustness for estimators is the finite-sample breakdown point (FSBP) (Donoho and Huber (1983)). Despite many attempts made in the literature, only sporadic partial results on FSBP for $\bs{\beta}^*_{RD}$ were obtained whereas an exact FSBP for $\bs{\beta}^*_{RD}$ remained open in the last twenty-plus years. Furthermore, is the asymptotic breakdown value $1/3$ (the limit of an increasing sequence of finite-sample breakdown values) relevant in the finite-sample practice? (Or what is the difference between the finite-sample and the limit breakdown values?). Such discussions are yet to be given in the literature. This article addresses the above issues, revealing an intrinsic connection between the regression depth of $\bs{\beta}^*_{RD}$ and the newly obtained exact FSBP. It justifies the employment of $\bs{\beta}^*_{RD}$ as a robust alternative to the traditional estimators and demonstrates the necessity and the merit of using the FSBP in finite-sample real practice.
The proliferation of Deep Learning (DL)-based methods for radiographic image analysis has created a great demand for expert-labeled radiology data. Recent self-supervised frameworks have alleviated the need for expert labeling by obtaining supervision from associated radiology reports. These frameworks, however, struggle to distinguish the subtle differences between different pathologies in medical images. Additionally, many of them do not provide interpretation between image regions and text, making it difficult for radiologists to assess model predictions. In this work, we propose Local Region Contrastive Learning (LRCLR), a flexible fine-tuning framework that adds layers for significant image region selection as well as cross-modality interaction. Our results on an external validation set of chest x-rays suggest that LRCLR identifies significant local image regions and provides meaningful interpretation against radiology text while improving zero-shot performance on several chest x-ray medical findings.
The Q-learning algorithm is known to be affected by the maximization bias, i.e. the systematic overestimation of action values, an important issue that has recently received renewed attention. Double Q-learning has been proposed as an efficient algorithm to mitigate this bias. However, this comes at the price of an underestimation of action values, in addition to increased memory requirements and a slower convergence. In this paper, we introduce a new way to address the maximization bias in the form of a "self-correcting algorithm" for approximating the maximum of an expected value. Our method balances the overestimation of the single estimator used in conventional Q-learning and the underestimation of the double estimator used in Double Q-learning. Applying this strategy to Q-learning results in Self-correcting Q-learning. We show theoretically that this new algorithm enjoys the same convergence guarantees as Q-learning while being more accurate. Empirically, it performs better than Double Q-learning in domains with rewards of high variance, and it even attains faster convergence than Q-learning in domains with rewards of zero or low variance. These advantages transfer to a Deep Q Network implementation that we call Self-correcting DQN and which outperforms regular DQN and Double DQN on several tasks in the Atari 2600 domain.
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