Kernel methods are learning algorithms that enjoy solid theoretical foundations while suffering from important computational limitations. Sketching, that consists in looking for solutions among a subspace of reduced dimension, is a widely studied approach to alleviate this numerical burden. However, fast sketching strategies, such as non-adaptive subsampling, significantly degrade the guarantees of the algorithms, while theoretically-accurate sketches, such as the Gaussian one, turn out to remain relatively slow in practice. In this paper, we introduce the $p$-sparsified sketches, that combine the benefits from both approaches to achieve a good tradeoff between statistical accuracy and computational efficiency. To support our method, we derive excess risk bounds for both single and multiple output problems, with generic Lipschitz losses, providing new guarantees for a wide range of applications, from robust regression to multiple quantile regression. We also provide empirical evidences of the superiority of our sketches over recent SOTA approaches.
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One of the recent developments in deep learning is generalized zero-shot learning (GZSL), which aims to recognize objects from both seen and unseen classes, when only the labeled examples from seen classes are provided. Over the past couple of years, GZSL has picked up traction and several models have been proposed to solve this problem. Whereas an extensive amount of research on GZSL has been carried out in fields such as computer vision and natural language processing, no such research has been carried out to deal with time series data. GZSL is used for applications such as detecting abnormalities from ECG and EEG data and identifying unseen classes from sensor, spectrograph and other devices' data. In this regard, we propose a Latent Embedding for Time Series - GZSL (LETS-GZSL) model that can solve the problem of GZSL for time series classification (TSC). We utilize an embedding-based approach and combine it with attribute vectors to predict the final class labels. We report our results on the widely popular UCR archive datasets. Our framework is able to achieve a harmonic mean value of at least 55% on most of the datasets except when the number of unseen classes is greater than 3 or the amount of data is very low (less than 100 training examples).
We study \textit{rescaled gradient dynamical systems} in a Hilbert space $\mathcal{H}$, where implicit discretization in a finite-dimensional Euclidean space leads to high-order methods for solving monotone equations (MEs). Our framework can be interpreted as a natural generalization of celebrated dual extrapolation method~\citep{Nesterov-2007-Dual} from first order to high order via appeal to the regularization toolbox of optimization theory~\citep{Nesterov-2021-Implementable, Nesterov-2021-Inexact}. More specifically, we establish the existence and uniqueness of a global solution and analyze the convergence properties of solution trajectories. We also present discrete-time counterparts of our high-order continuous-time methods, and we show that the $p^{th}$-order method achieves an ergodic rate of $O(k^{-(p+1)/2})$ in terms of a restricted merit function and a pointwise rate of $O(k^{-p/2})$ in terms of a residue function. Under regularity conditions, the restarted version of $p^{th}$-order methods achieves local convergence with the order $p \geq 2$. Notably, our methods are \textit{optimal} since they have matched the lower bound established for solving the monotone equation problems under a standard linear span assumption~\citep{Lin-2022-Perseus}.
There are good arguments to support the claim that deep neural networks (DNNs) capture better feature representations than the previous hand-crafted feature engineering, which leads to a significant performance improvement. In this paper, we move a tiny step towards understanding the dynamics of feature representations over layers. Specifically, we model the process of class separation of intermediate representations in pre-trained DNNs as the evolution of communities in dynamic graphs. Then, we introduce modularity, a generic metric in graph theory, to quantify the evolution of communities. In the preliminary experiment, we find that modularity roughly tends to increase as the layer goes deeper and the degradation and plateau arise when the model complexity is great relative to the dataset. Through an asymptotic analysis, we prove that modularity can be broadly used for different applications. For example, modularity provides new insights to quantify the difference between feature representations. More crucially, we demonstrate that the degradation and plateau in modularity curves represent redundant layers in DNNs and can be pruned with minimal impact on performance, which provides theoretical guidance for layer pruning. Our code is available at //github.com/yaolu-zjut/Dynamic-Graphs-Construction.
Multiple Tensor-Times-Matrix (Multi-TTM) is a key computation in algorithms for computing and operating with the Tucker tensor decomposition, which is frequently used in multidimensional data analysis. We establish communication lower bounds that determine how much data movement is required to perform the Multi-TTM computation in parallel. The crux of the proof relies on analytically solving a constrained, nonlinear optimization problem. We also present a parallel algorithm to perform this computation that organizes the processors into a logical grid with twice as many modes as the input tensor. We show that with correct choices of grid dimensions, the communication cost of the algorithm attains the lower bounds and is therefore communication optimal. Finally, we show that our algorithm can significantly reduce communication compared to the straightforward approach of expressing the computation as a sequence of tensor-times-matrix operations.
Gaussian processes have become a promising tool for various safety-critical settings, since the posterior variance can be used to directly estimate the model error and quantify risk. However, state-of-the-art techniques for safety-critical settings hinge on the assumption that the kernel hyperparameters are known, which does not apply in general. To mitigate this, we introduce robust Gaussian process uniform error bounds in settings with unknown hyperparameters. Our approach computes a confidence region in the space of hyperparameters, which enables us to obtain a probabilistic upper bound for the model error of a Gaussian process with arbitrary hyperparameters. We do not require to know any bounds for the hyperparameters a priori, which is an assumption commonly found in related work. Instead, we are able to derive bounds from data in an intuitive fashion. We additionally employ the proposed technique to derive performance guarantees for a class of learning-based control problems. Experiments show that the bound performs significantly better than vanilla and fully Bayesian Gaussian processes.
Deep neural models in recent years have been successful in almost every field, including extremely complex problem statements. However, these models are huge in size, with millions (and even billions) of parameters, thus demanding more heavy computation power and failing to be deployed on edge devices. Besides, the performance boost is highly dependent on redundant labeled data. To achieve faster speeds and to handle the problems caused by the lack of data, knowledge distillation (KD) has been proposed to transfer information learned from one model to another. KD is often characterized by the so-called `Student-Teacher' (S-T) learning framework and has been broadly applied in model compression and knowledge transfer. This paper is about KD and S-T learning, which are being actively studied in recent years. First, we aim to provide explanations of what KD is and how/why it works. Then, we provide a comprehensive survey on the recent progress of KD methods together with S-T frameworks typically for vision tasks. In general, we consider some fundamental questions that have been driving this research area and thoroughly generalize the research progress and technical details. Additionally, we systematically analyze the research status of KD in vision applications. Finally, we discuss the potentials and open challenges of existing methods and prospect the future directions of KD and S-T learning.
Graph Neural Networks (GNNs) have recently become increasingly popular due to their ability to learn complex systems of relations or interactions arising in a broad spectrum of problems ranging from biology and particle physics to social networks and recommendation systems. Despite the plethora of different models for deep learning on graphs, few approaches have been proposed thus far for dealing with graphs that present some sort of dynamic nature (e.g. evolving features or connectivity over time). In this paper, we present Temporal Graph Networks (TGNs), a generic, efficient framework for deep learning on dynamic graphs represented as sequences of timed events. Thanks to a novel combination of memory modules and graph-based operators, TGNs are able to significantly outperform previous approaches being at the same time more computationally efficient. We furthermore show that several previous models for learning on dynamic graphs can be cast as specific instances of our framework. We perform a detailed ablation study of different components of our framework and devise the best configuration that achieves state-of-the-art performance on several transductive and inductive prediction tasks for dynamic graphs.
Over the past few years, we have seen fundamental breakthroughs in core problems in machine learning, largely driven by advances in deep neural networks. At the same time, the amount of data collected in a wide array of scientific domains is dramatically increasing in both size and complexity. Taken together, this suggests many exciting opportunities for deep learning applications in scientific settings. But a significant challenge to this is simply knowing where to start. The sheer breadth and diversity of different deep learning techniques makes it difficult to determine what scientific problems might be most amenable to these methods, or which specific combination of methods might offer the most promising first approach. In this survey, we focus on addressing this central issue, providing an overview of many widely used deep learning models, spanning visual, sequential and graph structured data, associated tasks and different training methods, along with techniques to use deep learning with less data and better interpret these complex models --- two central considerations for many scientific use cases. We also include overviews of the full design process, implementation tips, and links to a plethora of tutorials, research summaries and open-sourced deep learning pipelines and pretrained models, developed by the community. We hope that this survey will help accelerate the use of deep learning across different scientific domains.
Object detection typically assumes that training and test data are drawn from an identical distribution, which, however, does not always hold in practice. Such a distribution mismatch will lead to a significant performance drop. In this work, we aim to improve the cross-domain robustness of object detection. We tackle the domain shift on two levels: 1) the image-level shift, such as image style, illumination, etc, and 2) the instance-level shift, such as object appearance, size, etc. We build our approach based on the recent state-of-the-art Faster R-CNN model, and design two domain adaptation components, on image level and instance level, to reduce the domain discrepancy. The two domain adaptation components are based on H-divergence theory, and are implemented by learning a domain classifier in adversarial training manner. The domain classifiers on different levels are further reinforced with a consistency regularization to learn a domain-invariant region proposal network (RPN) in the Faster R-CNN model. We evaluate our newly proposed approach using multiple datasets including Cityscapes, KITTI, SIM10K, etc. The results demonstrate the effectiveness of our proposed approach for robust object detection in various domain shift scenarios.
Learning from a few examples remains a key challenge in machine learning. Despite recent advances in important domains such as vision and language, the standard supervised deep learning paradigm does not offer a satisfactory solution for learning new concepts rapidly from little data. In this work, we employ ideas from metric learning based on deep neural features and from recent advances that augment neural networks with external memories. Our framework learns a network that maps a small labelled support set and an unlabelled example to its label, obviating the need for fine-tuning to adapt to new class types. We then define one-shot learning problems on vision (using Omniglot, ImageNet) and language tasks. Our algorithm improves one-shot accuracy on ImageNet from 87.6% to 93.2% and from 88.0% to 93.8% on Omniglot compared to competing approaches. We also demonstrate the usefulness of the same model on language modeling by introducing a one-shot task on the Penn Treebank.
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