NeurIPS 2023 论文列表

Conference on Neural Information Processing Systems

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3,584篇论文

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VTaC: A Benchmark Dataset of Ventricular Tachycardia Alarms from ICU Monitors

Li-wei H. Lehman, Benjamin E Moody, Harsh Deep, Feng Wu, Hasan Saeed, Lucas McCullum, Diane Perry, Tristan Struja, Qiao Li, Gari Clifford, Roger Mark

展开摘要

False arrhythmia alarms in intensive care units (ICUs) are a continuing problem despite considerable effort from industrial and academic algorithm developers. Of all life-threatening arrhythmias, ventricular tachycardia (VT) stands out as the most challenging arrhythmia to detect reliably. We introduce a new annotated VT alarm database, VTaC (Ventricular Tachycardia annotated alarms from ICUs) consisting of over 5,000 waveform recordings with VT alarms triggered by bedside monitors in the ICUs. Each VT alarm in the dataset has been labeled by at least two independent human expert annotators. The dataset encompasses data collected from ICUs in three major US hospitals and includes data from three leading bedside monitor manufacturers, providing a diverse and representative collection of alarm waveform data. Each waveform recording comprises at least two electrocardiogram (ECG) leads and one or more pulsatile waveforms, such as photoplethysmogram (PPG or PLETH) and arterial blood pressure (ABP) waveforms. We demonstrate the utility of this new benchmark dataset for the task of false arrhythmia alarm reduction, and present performance of multiple machine learning approaches, including conventional supervised machine learning, deep learning, contrastive learning and generative approaches for the task of VT false alarm reduction.

Poster
ANTN: Bridging Autoregressive Neural Networks and Tensor Networks for Quantum Many-Body Simulation

Zhuo Chen, Laker Newhouse, Eddie Chen, Di Luo, Marin Soljacic

展开摘要

Quantum many-body physics simulation has important impacts on understanding fundamental science and has applications to quantum materials design and quantum technology. However, due to the exponentially growing size of the Hilbert space with respect to the particle number, a direct simulation is intractable. While representing quantum states with tensor networks and neural networks are the two state-of-the-art methods for approximate simulations, each has its own limitations in terms of expressivity and inductive bias. To address these challenges, we develop a novel architecture, Autoregressive Neural TensorNet (ANTN), which bridges tensor networks and autoregressive neural networks. We show that Autoregressive Neural TensorNet parameterizes normalized wavefunctions, allows for exact sampling, generalizes the expressivity of tensor networks and autoregressive neural networks, and inherits a variety of symmetries from autoregressive neural networks. We demonstrate our approach on quantum state learning as well as finding the ground state of the challenging 2D $J_1$-$J_2$ Heisenberg model with different systems sizes and coupling parameters, outperforming both tensor networks and autoregressive neural networks. Our work opens up new opportunities for quantum many-body physics simulation, quantum technology design, and generative modeling in artificial intelligence.

Poster
Cross-Domain Policy Adaptation via Value-Guided Data Filtering

Kang Xu, Chenjia Bai, Xiaoteng Ma, Dong Wang, Bin Zhao, Zhen Wang, Xuelong Li, Wei Li

展开摘要

Generalizing policies across different domains with dynamics mismatch poses a significant challenge in reinforcement learning. For example, a robot learns the policy in a simulator, but when it is deployed in the real world, the dynamics of the environment may be different. Given the source and target domain with dynamics mismatch, we consider the online dynamics adaptation problem, in which case the agent can access sufficient source domain data while online interactions with the target domain are limited. Existing research has attempted to solve the problem from the dynamics discrepancy perspective. In this work, we reveal the limitations of these methods and explore the problem from the value difference perspective via a novel insight on the value consistency across domains. Specifically, we present the Value-Guided Data Filtering (VGDF) algorithm, which selectively shares transitions from the source domain based on the proximity of paired value targets across the two domains. Empirical results on various environments with kinematic and morphology shifts demonstrate that our method achieves superior performance compared to prior approaches.

Poster
Multi-Head Adapter Routing for Cross-Task Generalization

Lucas Caccia, Edoardo Ponti, Zhan Su, Matheus Pereira, Nicolas Le Roux, Alessandro Sordoni

展开摘要

Parameter-efficient fine-tuning (PEFT) for cross-task generalization consists in pre-training adapters on a multi-task training set before few-shot adaptation to test tasks. Polytropon [Ponti et al., 2023] ($\texttt{Poly}$) jointly learns an inventory of adapters and a *routing* function that selects a (variable-size) subset of adapters for each task during both pre-training and few-shot adaptation. In this paper, we investigate the role that adapter routing plays in its success and design new variants based on our findings. First, we build on the intuition that finer-grained routing provides more expressivity. Hence, we propose $\texttt{MHR}$ (Multi-Head Routing) which combines *subsets* of adapter parameters and outperforms $\texttt{Poly}$ under a comparable parameter budget; by only fine-tuning the routing function and not the adapters ($\texttt{MHR}$-$z$) we achieve competitive performance with extreme parameter efficiency. Second, we find that $\texttt{Poly}$/$\texttt{MHR}$ performance is a result of better multi-task optimization, rather than modular inductive biases that facilitate adapter recombination and local adaptation, as previously hypothesized. In fact, we find that $\texttt{MHR}$ exhibits high gradient alignment between training tasks. We find that routing is most beneficial during multi-task pre-training rather than during few-shot adaptation and propose $\texttt{MHR}$-$\mu$, which discards routing and fine-tunes the average of the pre-trained adapters on each downstream tasks. This establishes $\texttt{MHR}$-$\mu$ as an effective method for single-adapter fine-tuning. We also show that $\texttt{MHR}$-$\mu$ can be used as an effective zero-shot transfer method by training the average of the pre-trained adapters for a few additional steps on the multi-task training set: this yields gains up to 3\% on absolute accuracy w.r.t. the baselines. Code is available at <https://github.com/microsoft/mttl>.

Poster
One Risk to Rule Them All: A Risk-Sensitive Perspective on Model-Based Offline Reinforcement Learning

Marc Rigter, Bruno Lacerda, Nick Hawes

展开摘要

Offline reinforcement learning (RL) is suitable for safety-critical domains where online exploration is not feasible. In such domains, decision-making should take into consideration the risk of catastrophic outcomes. In other words, decision-making should be *risk-averse*. An additional challenge of offline RL is avoiding *distributional shift*, i.e. ensuring that state-action pairs visited by the policy remain near those in the dataset. Previous offline RL algorithms that consider risk combine offline RL techniques (to avoid distributional shift), with risk-sensitive RL algorithms (to achieve risk-aversion). In this work, we propose risk-aversion as a mechanism to jointly address *both* of these issues. We propose a model-based approach, and use an ensemble of models to estimate epistemic uncertainty, in addition to aleatoric uncertainty. We train a policy that is risk-averse, and avoids high uncertainty actions. Risk-aversion to epistemic uncertainty prevents distributional shift, as areas not covered by the dataset have high epistemic uncertainty. Risk-aversion to aleatoric uncertainty discourages actions that are risky due to environment stochasticity. Thus, by considering epistemic uncertainty via a model ensemble and introducing risk-aversion, our algorithm (1R2R) avoids distributional shift in addition to achieving risk-aversion to aleatoric risk. Our experiments show that 1R2R achieves strong performance on deterministic benchmarks, and outperforms existing approaches for risk-sensitive objectives in stochastic domains.

Poster
Multi-Objective Intrinsic Reward Learning for Conversational Recommender Systems

Zhendong Chu, Nan Wang, Hongning Wang

展开摘要

Conversational Recommender Systems (CRS) actively elicit user preferences to generate adaptive recommendations. Mainstream reinforcement learning-based CRS solutions heavily rely on handcrafted reward functions, which may not be aligned with user intent in CRS tasks. Therefore, the design of task-specific rewards is critical to facilitate CRS policy learning, which remains largely under-explored in the literature. In this work, we propose a novel approach to address this challenge by learning intrinsic rewards from interactions with users. Specifically, we formulate intrinsic reward learning as a multi-objective bi-level optimization problem. The inner level optimizes the CRS policy augmented by the learned intrinsic rewards, while the outer level drives the intrinsic rewards to optimize two CRS-specific objectives: maximizing the success rate and minimizing the number of turns to reach a successful recommendation}in conversations. To evaluate the effectiveness of our approach, we conduct extensive experiments on three public CRS benchmarks. The results show that our algorithm significantly improves CRS performance by exploiting informative learned intrinsic rewards.

Poster
Are GATs Out of Balance?

Nimrah Mustafa, Aleksandar Bojchevski, Rebekka Burkholz

展开摘要

While the expressive power and computational capabilities of graph neural networks (GNNs) have been theoretically studied, their optimization and learning dynamics, in general, remain largely unexplored. Our study undertakes the Graph Attention Network (GAT), a popular GNN architecture in which a node's neighborhood aggregation is weighted by parameterized attention coefficients. We derive a conservation law of GAT gradient flow dynamics, which explains why a high portion of parameters in GATs with standard initialization struggle to change during training. This effect is amplified in deeper GATs, which perform significantly worse than their shallow counterparts. To alleviate this problem, we devise an initialization scheme that balances the GAT network. Our approach i) allows more effective propagation of gradients and in turn enables trainability of deeper networks, and ii) attains a considerable speedup in training and convergence time in comparison to the standard initialization. Our main theorem serves as a stepping stone to studying the learning dynamics of positive homogeneous models with attention mechanisms.

Poster
StressID: a Multimodal Dataset for Stress Identification

Hava Chaptoukaev, Valeriya Strizhkova, Michele Panariello, Bianca Dalpaos, Aglind Reka, Valeria Manera, Susanne Thummler, Esma ISMAILOVA, Nicholas Evans, Francois Bremond, Massimiliano Todisco, Maria A Zuluaga, Laura M. Ferrari

展开摘要

StressID is a new dataset specifically designed for stress identification from unimodal and multimodal data. It contains videos of facial expressions, audio recordings, and physiological signals. The video and audio recordings are acquired using an RGB camera with an integrated microphone. The physiological data is composed of electrocardiography (ECG), electrodermal activity (EDA), and respiration signals that are recorded and monitored using a wearable device. This experimental setup ensures a synchronized and high-quality multimodal data col- lection. Different stress-inducing stimuli, such as emotional video clips, cognitive tasks including mathematical or comprehension exercises, and public speaking scenarios, are designed to trigger a diverse range of emotional responses. The final dataset consists of recordings from 65 participants who performed 11 tasks, as well as their ratings of perceived relaxation, stress, arousal, and valence levels. StressID is one of the largest datasets for stress identification that features three different sources of data and varied classes of stimuli, representing more than 39 hours of annotated data in total. StressID offers baseline models for stress classification including a cleaning, feature extraction, and classification phase for each modality. Additionally, we provide multimodal predictive models combining video, audio, and physiological inputs. The data and the code for the baselines are available at https://project.inria.fr/stressid/.

Poster
CoPriv: Network/Protocol Co-Optimization for Communication-Efficient Private Inference

Wenxuan Zeng, Meng Li, Haichuan Yang, Wen-jie Lu, Runsheng Wang, Ru Huang

展开摘要

Deep neural network (DNN) inference based on secure 2-party computation (2PC) can offer cryptographically-secure privacy protection but suffers from orders of magnitude latency overhead due to enormous communication. Previous works heavily rely on a proxy metric of ReLU counts to approximate the communication overhead and focus on reducing the ReLUs to improve the communication efficiency. However, we observe these works achieve limited communication reduction for state-of-the-art (SOTA) 2PC protocols due to the ignorance of other linear and non-linear operations, which now contribute to the majority of communication. In this work, we present CoPriv, a framework that jointly optimizes the 2PC inference protocol and the DNN architecture. CoPriv features a new 2PC protocol for convolution based on Winograd transformation and develops DNN-aware optimization to significantly reduce the inference communication. CoPriv further develops a 2PC-aware network optimization algorithm that is compatible with the proposed protocol and simultaneously reduces the communication for all the linear and non-linear operations. We compare CoPriv with the SOTA 2PC protocol, CrypTFlow2, and demonstrate 2.1× communication reduction for both ResNet-18 and ResNet-32 on CIFAR-100. We also compare CoPriv with SOTA network optimization methods, including SNL, MetaPruning, etc. CoPriv achieves 9.98× and 3.88× online and total communication reduction with a higher accuracy compare to SNL, respectively. CoPriv also achieves 3.87× online communication reduction with more than 3% higher accuracy compared to MetaPruning.

Poster
LambdaBeam: Neural Program Search with Higher-Order Functions and Lambdas

Kensen Shi, Hanjun Dai, Wen-Ding Li, Kevin Ellis, Charles Sutton

展开摘要

Search is an important technique in program synthesis that allows for adaptive strategies such as focusing on particular search directions based on execution results. Several prior works have demonstrated that neural models are effective at guiding program synthesis searches. However, a common drawback of those approaches is the inability to handle iterative loops, higher-order functions, or lambda functions, thus limiting prior neural searches from synthesizing longer and more general programs. We address this gap by designing a search algorithm called LambdaBeam that can construct arbitrary lambda functions that compose operations within a given DSL. We create semantic vector representations of the execution behavior of the lambda functions and train a neural policy network to choose which lambdas to construct during search, and pass them as arguments to higher-order functions to perform looping computations. Our experiments show that LambdaBeam outperforms neural, symbolic, and LLM-based techniques in an integer list manipulation domain.

Poster
Multi-resolution Spectral Coherence for Graph Generation with Score-based Diffusion

Hyuna Cho, Minjae Jeong, Sooyeon Jeon, Sungsoo Ahn, Won Hwa Kim

展开摘要

Successful graph generation depends on the accurate estimation of the joint distribution of graph components such as nodes and edges from training data. While recent deep neural networks have demonstrated sampling of realistic graphs together with diffusion models, however, they still suffer from oversmoothing problems which are inherited from conventional graph convolution and thus high-frequency characteristics of nodes and edges become intractable. To overcome such issues and generate graphs with high fidelity, this paper introduces a novel approach that captures the dependency between nodes and edges at multiple resolutions in the spectral space. By modeling the joint distribution of node and edge signals in a shared graph wavelet space, together with a score-based diffusion model, we propose a Wavelet Graph Diffusion Model (Wave-GD) which lets us sample synthetic graphs with real-like frequency characteristics of nodes and edges. Experimental results on four representative benchmark datasets validate the superiority of the Wave-GD over existing approaches, highlighting its potential for a wide range of applications that involve graph data.

Poster
The Double-Edged Sword of Implicit Bias: Generalization vs. Robustness in ReLU Networks

Spencer Frei, Gal Vardi, Peter Bartlett, Nathan Srebro

展开摘要

In this work, we study the implications of the implicit bias of gradient flow on generalization and adversarial robustness in ReLU networks. We focus on a setting where the data consists of clusters and the correlations between cluster means are small, and show that in two-layer ReLU networks gradient flow is biased towards solutions that generalize well, but are vulnerable to adversarial examples. Our results hold even in cases where the network is highly overparameterized. Despite the potential for harmful overfitting in such settings, we prove that the implicit bias of gradient flow prevents it. However, the implicit bias also leads to non-robust solutions (susceptible to small adversarial $\ell_2$-perturbations), even though robust networks that fit the data exist.

Poster
Provably Efficient Offline Goal-Conditioned Reinforcement Learning with General Function Approximation and Single-Policy Concentrability

Hanlin Zhu, Amy Zhang

展开摘要

Goal-conditioned reinforcement learning (GCRL) refers to learning general-purpose skills that aim to reach diverse goals. In particular, offline GCRL only requires purely pre-collected datasets to perform training tasks without additional interactions with the environment. Although offline GCRL has become increasingly prevalent and many previous works have demonstrated its empirical success, the theoretical understanding of efficient offline GCRL algorithms is not well established, especially when the state space is huge and the offline dataset only covers the policy we aim to learn. In this paper, we provide a rigorous theoretical analysis of an existing empirically successful offline GCRL algorithm. We prove that under slight modification, this algorithm enjoys an $\tilde{O}(\text{poly}(1/\epsilon))$ sample complexity (where $\epsilon$ is the desired suboptimality of the learned policy) with general function approximation thanks to the property of (semi-)strong convexity of the objective functions. We only require nearly minimal assumptions on the dataset (single-policy concentrability) and the function class (realizability). Moreover, this algorithm consists of two uninterleaved optimization steps, which we refer to as $V$-learning and policy learning, and is computationally stable since it does not involve minimax optimization. We also empirically validate our theory by showing that the modified algorithm outperforms the previous algorithm in various real-world environments. To the best of our knowledge, this is the first algorithm that is both provably efficient with general function approximation and single-policy concentrability, and empirically successful without requiring solving minimax optimization problems.

Poster
Complex Query Answering on Eventuality Knowledge Graph with Implicit Logical Constraints

Jiaxin Bai, Xin Liu, Weiqi Wang, Chen Luo, Yangqiu Song

展开摘要

Querying knowledge graphs (KGs) using deep learning approaches can naturally leverage the reasoning and generalization ability to learn to infer better answers. Traditional neural complex query answering (CQA) approaches mostly work on entity-centric KGs. However, in the real world, we also need to make logical inferences about events, states, and activities (i.e., eventualities or situations) to push learning systems from System I to System II, as proposed by Yoshua Bengio. Querying logically from an EVentuality-centric KG (EVKG) can naturally provide references to such kind of intuitive and logical inference. Thus, in this paper, we propose a new framework to leverage neural methods to answer complex logical queries based on an EVKG, which can satisfy not only traditional first-order logic constraints but also implicit logical constraints over eventualities concerning their occurrences and orders. For instance, if we know that *Food is bad* happens before *PersonX adds soy sauce*, then *PersonX adds soy sauce* is unlikely to be the cause of *Food is bad* due to implicit temporal constraint. To facilitate consistent reasoning on EVKGs, we propose Complex Eventuality Query Answering (CEQA), a more rigorous definition of CQA that considers the implicit logical constraints governing the temporal order and occurrence of eventualities. In this manner, we propose to leverage theorem provers for constructing benchmark datasets to ensure the answers satisfy implicit logical constraints. We also propose a Memory-Enhanced Query Encoding (MEQE) approach to significantly improve the performance of state-of-the-art neural query encoders on the CEQA task.

Poster
Statistical Insights into HSIC in High Dimensions

Tao Zhang, Yaowu Zhang, Tingyou Zhou

展开摘要

Measuring the nonlinear dependence between random vectors and testing for their statistical independence is a fundamental problem in statistics. One of the most popular dependence measures is the Hilbert-Schmidt independence criterion (HSIC), which has attracted increasing attention in recent years. However, most existing works have focused on either fixed or very high-dimensional covariates. In this work, we bridge the gap between these two scenarios and provide statistical insights into the performance of HSIC when the dimensions grow at different rates. We first show that, under the null hypothesis, the rescaled HSIC converges in distribution to a standard normal distribution. Then we provide a general condition for the HSIC based tests to have nontrivial power in high dimensions. By decomposing this condition, we illustrate how the ability of HSIC to measure nonlinear dependence changes with increasing dimensions. Moreover, we demonstrate that, depending on the sample size, the covariate dimensions and the dependence structures within covariates, the HSIC can capture different types of associations between random vectors. We also conduct extensive numerical studies to validate our theoretical results.

Poster
Monitor-Guided Decoding of Code LMs with Static Analysis of Repository Context

Lakshya Agrawal, Aditya Kanade, Navin Goyal, Shuvendu K Lahiri, Sriram Rajamani

展开摘要

Language models of code (LMs) work well when the surrounding code provides sufficient context. This is not true when it becomes necessary to use types, functionality or APIs defined elsewhere in the repository or a linked library, especially those not seen during training. LMs suffer from limited awareness of such global context and end up hallucinating. Integrated development environments (IDEs) assist developers in understanding repository context using static analysis. We extend this assistance, enjoyed by developers, to LMs. We propose monitor-guided decoding (MGD) where a monitor uses static analysis to guide the decoding. We construct a repository-level dataset PragmaticCode for method-completion in Java and evaluate MGD on it. On models of varying parameter scale, by monitoring for type-consistent object dereferences, MGD consistently improves compilation rates and agreement with ground truth. Further, LMs with fewer parameters, when augmented with MGD, can outperform larger LMs. With MGD, SantaCoder-1.1B achieves better compilation rate and next-identifier match than the much larger text-davinci-003 model. We also conduct a generalizability study to evaluate the ability of MGD to generalize to multiple programming languages (Java, C# and Rust), coding scenarios (e.g., correct number of arguments to method calls), and to enforce richer semantic constraints (e.g., stateful API protocols). Our data and implementation are available at https://github.com/microsoft/monitors4codegen.

Poster
Read and Reap the Rewards: Learning to Play Atari with the Help of Instruction Manuals

Yue Wu, Yewen Fan, Paul Pu Liang, Amos Azaria, Yuanzhi Li, Tom Mitchell

展开摘要

High sample complexity has long been a challenge for RL. On the other hand, humans learn to perform tasks not only from interaction or demonstrations, but also by reading unstructured text documents, e.g., instruction manuals. Instruction manuals and wiki pages are among the most abundant data that could inform agents of valuable features and policies or task-specific environmental dynamics and reward structures. Therefore, we hypothesize that the ability to utilize human-written instruction manuals to assist learning policies for specific tasks should lead to a more efficient and better-performing agent. We propose the Read and Reward framework. Read and Reward speeds up RL algorithms on Atari games by reading manuals released by the Atari game developers. Our framework consists of a QA Extraction module that extracts and summarizes relevant information from the manual and a Reasoning module that evaluates object-agent interactions based on information from the manual. An auxiliary reward is then provided to a standard A2C RL agent, when interaction is detected. Experimentally, various RL algorithms obtain significant improvement in performance and training speed when assisted by our design. Code at github.com/Holmeswww/RnR

Poster
TriRE: A Multi-Mechanism Learning Paradigm for Continual Knowledge Retention and Promotion

Preetha Vijayan, Prashant Shivaram Bhat, Bahram Zonooz, Elahe Arani

展开摘要

Continual learning (CL) has remained a persistent challenge for deep neural networks due to catastrophic forgetting (CF) of previously learned tasks. Several techniques such as weight regularization, experience rehearsal, and parameter isolation have been proposed to alleviate CF. Despite their relative success, these research directions have predominantly remained orthogonal and suffer from several shortcomings, while missing out on the advantages of competing strategies. On the contrary, the brain continually learns, accommodates, and transfers knowledge across tasks by simultaneously leveraging several neurophysiological processes, including neurogenesis, active forgetting, neuromodulation, metaplasticity, experience rehearsal, and context-dependent gating, rarely resulting in CF. Inspired by how the brain exploits multiple mechanisms concurrently, we propose TriRE, a novel CL paradigm that encompasses retaining the most prominent neurons for each task, revising and solidifying the extracted knowledge of current and past tasks, and actively promoting less active neurons for subsequent tasks through rewinding and relearning. Across CL settings, TriRE significantly reduces task interference and surpasses different CL approaches considered in isolation.

Poster
Is Heterogeneity Notorious? Taming Heterogeneity to Handle Test-Time Shift in Federated Learning

Yue Tan, Chen Chen, Weiming Zhuang, Xin Dong, Lingjuan Lyu, Guodong Long

展开摘要

Federated learning (FL) is an effective machine learning paradigm where multiple clients can train models based on heterogeneous data in a decentralized manner without accessing their private data. However, existing FL systems undergo performance deterioration due to feature-level test-time shifts, which are well investigated in centralized settings but rarely studied in FL. The common non-IID issue in FL usually refers to inter-client heterogeneity during training phase, while the test-time shift refers to the intra-client heterogeneity during test phase. Although the former is always deemed to be notorious for FL, there is still a wealth of useful information delivered by heterogeneous data sources, which may potentially help alleviate the latter issue. To explore the possibility of using inter-client heterogeneity in handling intra-client heterogeneity, we firstly propose a contrastive learning-based FL framework, namely FedICON, to capture invariant knowledge among heterogeneous clients and consistently tune the model to adapt to test data. In FedICON, each client performs sample-wise supervised contrastive learning during the local training phase, which enhances sample-wise invariance encoding ability. Through global aggregation, the invariance extraction ability can be mutually boosted among inter-client heterogeneity. During the test phase, our test-time adaptation procedure leverages unsupervised contrastive learning to guide the model to smoothly generalize to test data under intra-client heterogeneity. Extensive experiments validate the effectiveness of the proposed FedICON in taming heterogeneity to handle test-time shift problems.

Poster
Sketching Algorithms for Sparse Dictionary Learning: PTAS and Turnstile Streaming

Gregory Dexter, Petros Drineas, David Woodruff, Taisuke Yasuda

展开摘要

Sketching algorithms have recently proven to be a powerful approach both for designing low-space streaming algorithms as well as fast polynomial time approximation schemes (PTAS). In this work, we develop new techniques to extend the applicability of sketching-based approaches to the sparse dictionary learning and the Euclidean $k$-means clustering problems. In particular, we initiate the study of the challenging setting where the dictionary/clustering assignment for each of the $n$ input points must be output, which has surprisingly received little attention in prior work. On the fast algorithms front, we obtain a new approach for designing PTAS's for the $k$-means clustering problem, which generalizes to the first PTAS for the sparse dictionary learning problem. On the streaming algorithms front, we obtain new upper bounds and lower bounds for dictionary learning and $k$-means clustering. In particular, given a design matrix $\mathbf A\in\mathbb R^{n\times d}$ in a turnstile stream, we show an $\tilde O(nr/\epsilon^2 + dk/\epsilon)$ space upper bound for $r$-sparse dictionary learning of size $k$, an $\tilde O(n/\epsilon^2 + dk/\epsilon)$ space upper bound for $k$-means clustering, as well as an $\tilde O(n)$ space upper bound for $k$-means clustering on random order row insertion streams with a natural "bounded sensitivity" assumption. On the lower bounds side, we obtain a general $\tilde\Omega(n/\epsilon + dk/\epsilon)$ lower bound for $k$-means clustering, as well as an $\tilde\Omega(n/\epsilon^2)$ lower bound for algorithms which can estimate the cost of a single fixed set of candidate centers.

Poster