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Found 145 papers, 54 papers with code
A Three-regime Model of Network Pruning
Our approach uses temperature-like and load-like parameters to model the impact of neural network (NN) training hyperparameters on pruning performance.
Constrained Optimization via Exact Augmented Lagrangian and Randomized Iterative Sketching
Our method adaptively controls the accuracy of the randomized solver and the penalty parameters of the exact augmented Lagrangian, to ensure that the inexact Newton direction is a descent direction of the exact augmented Lagrangian.
When are ensembles really effective?
Ensembling has a long history in statistical data analysis, with many impactful applications.
End-to-end codesign of Hessian-aware quantized neural networks for FPGAs and ASICs
We develop an end-to-end workflow for the training and implementation of co-designed neural networks (NNs) for efficient field-programmable gate array (FPGA) and application-specific integrated circuit (ASIC) hardware.
Full Stack Optimization of Transformer Inference: a Survey
In this work, we survey different approaches for efficient Transformer inference, including: (i) analysis and profiling of the bottlenecks in existing Transformer architectures and their similarities and differences with previous convolutional models; (ii) implications of Transformer architecture on hardware, including the impact of non-linear operations such as Layer Normalization, Softmax, and GELU, as well as linear operations, on hardware design; (iii) approaches for optimizing a fixed Transformer architecture; (iv) challenges in finding the right mapping and scheduling of operations for Transformer models; and (v) approaches for optimizing Transformer models by adapting the architecture using neural architecture search.
Learning Physical Models that Can Respect Conservation Laws
We provide a detailed analysis of ProbConserv on learning with the Generalized Porous Medium Equation (GPME), a widely-applicable parameterized family of PDEs that illustrates the qualitative properties of both easier and harder PDEs.
Big Little Transformer Decoder
To address this, we propose Big Little Decoder (BiLD), a framework that can improve inference efficiency and latency for a wide range of text generation applications.
Gated Recurrent Neural Networks with Weighted Time-Delay Feedback
We prove the existence and uniqueness of solutions for the continuous-time model, and we demonstrate that the proposed feedback mechanism can help improve the modeling of long-term dependencies.
Fully Stochastic Trust-Region Sequential Quadratic Programming for Equality-Constrained Optimization Problems
We propose a trust-region stochastic sequential quadratic programming algorithm (TR-StoSQP) to solve nonlinear optimization problems with stochastic objectives and deterministic equality constraints.
Monotonicity and Double Descent in Uncertainty Estimation with Gaussian Processes
The quality of many modern machine learning models improves as model complexity increases, an effect that has been quantified, for predictive performance, with the non-monotonic double descent learning curve.
Gradient Gating for Deep Multi-Rate Learning on Graphs
We present Gradient Gating (G$^2$), a novel framework for improving the performance of Graph Neural Networks (GNNs).
Ranked #2 on
Node Classification
on arXiv-year
Learning differentiable solvers for systems with hard constraints
Our method leverages differentiable optimization and the implicit function theorem to effectively enforce physical constraints.
Adaptive Self-supervision Algorithms for Physics-informed Neural Networks
We find that training vanilla PINNs for these problems can result in up to 70% prediction error in the solution, especially in the regime of low collocation points.
Neurotoxin: Durable Backdoors in Federated Learning
In this type of attack, the goal of the attacker is to use poisoned updates to implant so-called backdoors into the learned model such that, at test time, the model's outputs can be fixed to a given target for certain inputs.
Squeezeformer: An Efficient Transformer for Automatic Speech Recognition
After re-examining the design choices for both the macro and micro-architecture of Conformer, we propose Squeezeformer which consistently outperforms the state-of-the-art ASR models under the same training schemes.
Ranked #27 on
Speech Recognition
on LibriSpeech test-clean
Automatic Speech Recognition
Automatic Speech Recognition (ASR)
Asymptotic Convergence Rate and Statistical Inference for Stochastic Sequential Quadratic Programming
We apply a stochastic sequential quadratic programming (StoSQP) algorithm to solve constrained nonlinear optimization problems, where the objective is stochastic and the constraints are deterministic.
Fat-Tailed Variational Inference with Anisotropic Tail Adaptive Flows
While fat-tailed densities commonly arise as posterior and marginal distributions in robust models and scale mixtures, they present challenges when Gaussian-based variational inference fails to capture tail decay accurately.
Hessian Averaging in Stochastic Newton Methods Achieves Superlinear Convergence
Remarkably, we show that there exists a universal weighted averaging scheme that transitions to local convergence at an optimal stage, and still exhibits a superlinear convergence rate nearly (up to a logarithmic factor) matching that of uniform Hessian averaging.
A Fast Post-Training Pruning Framework for Transformers
To address this, we propose a fast post-training pruning framework for Transformers that does not require any retraining.
Fast Feature Selection with Fairness Constraints
We study the fundamental problem of selecting optimal features for model construction.
Learning continuous models for continuous physics
A core issue with this approach is that ML models are typically trained on discrete data, using ML methodologies that are not aware of underlying continuity properties, which results in models that often do not capture the underlying continuous dynamics of a system of interest.
Evaluating natural language processing models with generalization metrics that do not need access to any training or testing data
We also show that among the three HT distributions considered in our paper, the E-TPL fitting of ESDs performs the most robustly when the models are trained in experimental settings, while the PL fitting achieves the best performance on well-trained Huggingface models, and that both E-TPL and PL metrics (which are both shape metrics) outperform scale metrics.
NoisyMix: Boosting Model Robustness to Common Corruptions
For many real-world applications, obtaining stable and robust statistical performance is more important than simply achieving state-of-the-art predictive test accuracy, and thus robustness of neural networks is an increasingly important topic.
Learning from learning machines: a new generation of AI technology to meet the needs of science
We outline emerging opportunities and challenges to enhance the utility of AI for scientific discovery.
Long Expressive Memory for Sequence Modeling
We propose a novel method called Long Expressive Memory (LEM) for learning long-term sequential dependencies.
Ranked #1 on
Time Series Classification
on EigenWorms
Noisy Feature Mixup
We introduce Noisy Feature Mixup (NFM), an inexpensive yet effective method for data augmentation that combines the best of interpolation based training and noise injection schemes.
Doubly Adaptive Scaled Algorithm for Machine Learning Using Second-Order Information
We present a novel adaptive optimization algorithm for large-scale machine learning problems.
What's Hidden in a One-layer Randomly Weighted Transformer?
Hidden within a one-layer randomly weighted Transformer, we find that subnetworks that can achieve 29. 45/17. 29 BLEU on IWSLT14/WMT14.
Characterizing possible failure modes in physics-informed neural networks
We provide evidence that the soft regularization in PINNs, which involves PDE-based differential operators, can introduce a number of subtle problems, including making the problem more ill-conditioned.
Generalization Bounds using Lower Tail Exponents in Stochastic Optimizers
Despite the ubiquitous use of stochastic optimization algorithms in machine learning, the precise impact of these algorithms and their dynamics on generalization performance in realistic non-convex settings is still poorly understood.
Taxonomizing local versus global structure in neural network loss landscapes
Viewing neural network models in terms of their loss landscapes has a long history in the statistical mechanics approach to learning, and in recent years it has received attention within machine learning proper.
Newton-LESS: Sparsification without Trade-offs for the Sketched Newton Update
In second-order optimization, a potential bottleneck can be computing the Hessian matrix of the optimized function at every iteration.
Stateful ODE-Nets using Basis Function Expansions
The recently-introduced class of ordinary differential equation networks (ODE-Nets) establishes a fruitful connection between deep learning and dynamical systems.
Post-mortem on a deep learning contest: a Simpson's paradox and the complementary roles of scale metrics versus shape metrics
Our results highlight the subtlety of comparing models when both architectures and hyperparameters are varied; the complementary role of implicit scale versus implicit shape parameters in understanding NN model quality; and the need to go beyond one-size-fits-all metrics based on upper bounds from generalization theory to describe the performance of NN models.
LEAP: Learnable Pruning for Transformer-based Models
Moreover, in order to reduce hyperparameter tuning, a novel adaptive regularization coefficient is deployed to control the regularization penalty adaptively.
ActNN: Reducing Training Memory Footprint via 2-Bit Activation Compressed Training
On all these tasks, ActNN compresses the activation to 2 bits on average, with negligible accuracy loss.
Integer-only Zero-shot Quantization for Efficient Speech Recognition
End-to-end neural network models achieve improved performance on various automatic speech recognition (ASR) tasks.
Automatic Speech Recognition
Automatic Speech Recognition (ASR)
+2
A Survey of Quantization Methods for Efficient Neural Network Inference
Thus, it is not surprising that quantization has emerged recently as an important and very active sub-area of research in the efficient implementation of computations associated with Neural Networks.
Hessian Eigenspectra of More Realistic Nonlinear Models
Given an optimization problem, the Hessian matrix and its eigenspectrum can be used in many ways, ranging from designing more efficient second-order algorithms to performing model analysis and regression diagnostics.
A Differential Geometry Perspective on Orthogonal Recurrent Models
In this work, we employ tools and insights from differential geometry to offer a novel perspective on orthogonal RNNs.
Noisy Recurrent Neural Networks
We provide a general framework for studying recurrent neural networks (RNNs) trained by injecting noise into hidden states.
I-BERT: Integer-only BERT Quantization
Transformer based models, like BERT and RoBERTa, have achieved state-of-the-art results in many Natural Language Processing tasks.
Natural Language Inference
Natural Language Understanding
+1
Improved guarantees and a multiple-descent curve for Column Subset Selection and the Nystrom method
The Column Subset Selection Problem (CSSP) and the Nystrom method are among the leading tools for constructing small low-rank approximations of large datasets in machine learning and scientific computing.
Sparse sketches with small inversion bias
For a tall $n\times d$ matrix $A$ and a random $m\times n$ sketching matrix $S$, the sketched estimate of the inverse covariance matrix $(A^\top A)^{-1}$ is typically biased: $E[(\tilde A^\top\tilde A)^{-1}]\ne(A^\top A)^{-1}$, where $\tilde A=SA$.
HAWQV3: Dyadic Neural Network Quantization
Current low-precision quantization algorithms often have the hidden cost of conversion back and forth from floating point to quantized integer values.
A Statistical Framework for Low-bitwidth Training of Deep Neural Networks
We show that the FQT gradient is an unbiased estimator of the QAT gradient, and we discuss the impact of gradient quantization on its variance.
Training Recommender Systems at Scale: Communication-Efficient Model and Data Parallelism
This is done by identifying and updating only the most relevant neurons of the neural network for each training sample in the data.
MAF: Multimodal Alignment Framework for Weakly-Supervised Phrase Grounding
Phrase localization is a task that studies the mapping from textual phrases to regions of an image.
Sparse Quantized Spectral Clustering
Given a large data matrix, sparsifying, quantizing, and/or performing other entry-wise nonlinear operations can have numerous benefits, ranging from speeding up iterative algorithms for core numerical linear algebra problems to providing nonlinear filters to design state-of-the-art neural network models.
Improving Semi-supervised Federated Learning by Reducing the Gradient Diversity of Models
Replacing BN with the recently-proposed Group Normalization (GN) can reduce gradient diversity and improve test accuracy.
Continuous-in-Depth Neural Networks
We first show that ResNets fail to be meaningful dynamical integrators in this richer sense.
Noise-Response Analysis of Deep Neural Networks Quantifies Robustness and Fingerprints Structural Malware
The ubiquity of deep neural networks (DNNs), cloud-based training, and transfer learning is giving rise to a new cybersecurity frontier in which unsecure DNNs have `structural malware' (i. e., compromised weights and activation pathways).
Adversarially-Trained Deep Nets Transfer Better: Illustration on Image Classification
Transfer learning has emerged as a powerful methodology for adapting pre-trained deep neural networks on image recognition tasks to new domains.
Boundary thickness and robustness in learning models
Using these observations, we show that noise-augmentation on mixup training further increases boundary thickness, thereby combating vulnerability to various forms of adversarial attacks and OOD transforms.
Debiasing Distributed Second Order Optimization with Surrogate Sketching and Scaled Regularization
In distributed second order optimization, a standard strategy is to average many local estimates, each of which is based on a small sketch or batch of the data.
Good Classifiers are Abundant in the Interpolating Regime
Inspired by the statistical mechanics approach to learning, we formally define and develop a methodology to compute precisely the full distribution of test errors among interpolating classifiers from several model classes.
Lipschitz Recurrent Neural Networks
Viewing recurrent neural networks (RNNs) as continuous-time dynamical systems, we propose a recurrent unit that describes the hidden state's evolution with two parts: a well-understood linear component plus a Lipschitz nonlinearity.
Precise expressions for random projections: Low-rank approximation and randomized Newton
It is often desirable to reduce the dimensionality of a large dataset by projecting it onto a low-dimensional subspace.
Multiplicative noise and heavy tails in stochastic optimization
Although stochastic optimization is central to modern machine learning, the precise mechanisms underlying its success, and in particular, the precise role of the stochasticity, still remain unclear.
A Random Matrix Analysis of Random Fourier Features: Beyond the Gaussian Kernel, a Precise Phase Transition, and the Corresponding Double Descent
This article characterizes the exact asymptotics of random Fourier feature (RFF) regression, in the realistic setting where the number of data samples $n$, their dimension $p$, and the dimension of feature space $N$ are all large and comparable.
ADAHESSIAN: An Adaptive Second Order Optimizer for Machine Learning
We introduce ADAHESSIAN, a second order stochastic optimization algorithm which dynamically incorporates the curvature of the loss function via ADAptive estimates of the HESSIAN.
Determinantal Point Processes in Randomized Numerical Linear Algebra
For example, random sampling with a DPP leads to new kinds of unbiased estimators for least squares, enabling more refined statistical and inferential understanding of these algorithms; a DPP is, in some sense, an optimal randomized algorithm for the Nystr\"om method; and a RandNLA technique called leverage score sampling can be derived as the marginal distribution of a DPP.
PowerNorm: Rethinking Batch Normalization in Transformers
To address this, we propose Power Normalization (PN), a novel normalization scheme that resolves this issue by (i) relaxing zero-mean normalization in BN, (ii) incorporating a running quadratic mean instead of per batch statistics to stabilize fluctuations, and (iii) using an approximate backpropagation for incorporating the running statistics in the forward pass.
Ranked #12 on
Machine Translation
on WMT2014 English-German
Error Estimation for Sketched SVD via the Bootstrap
In order to compute fast approximations to the singular value decompositions (SVD) of very large matrices, randomized sketching algorithms have become a leading approach.
Forecasting Sequential Data using Consistent Koopman Autoencoders
Recurrent neural networks are widely used on time series data, yet such models often ignore the underlying physical structures in such sequences.
Asymptotic Analysis of Sampling Estimators for Randomized Numerical Linear Algebra Algorithms
In this article, we develop an asymptotic analysis to derive the distribution of RandNLA sampling estimators for the least-squares problem.
Stochastic Normalizing Flows
We introduce stochastic normalizing flows, an extension of continuous normalizing flows for maximum likelihood estimation and variational inference (VI) using stochastic differential equations (SDEs).
Improved guarantees and a multiple-descent curve for Column Subset Selection and the Nyström method
The Column Subset Selection Problem (CSSP) and the Nystr\"om method are among the leading tools for constructing small low-rank approximations of large datasets in machine learning and scientific computing.
Predicting trends in the quality of state-of-the-art neural networks without access to training or testing data
We find that norm based metrics correlate well with reported test accuracies for well-trained models, but that they often cannot distinguish well-trained versus poorly-trained models.
ZeroQ: A Novel Zero Shot Quantization Framework
Importantly, ZeroQ has a very low computational overhead, and it can finish the entire quantization process in less than 30s (0. 5\% of one epoch training time of ResNet50 on ImageNet).
Ranked #1 on
Data Free Quantization
on CIFAR10
(CIFAR-10 W8A8 Top-1 Accuracy metric)
Exact expressions for double descent and implicit regularization via surrogate random design
We provide the first exact non-asymptotic expressions for double descent of the minimum norm linear estimator.
ANODEV2: A Coupled Neural ODE Framework
It has been observed that residual networks can be viewed as the explicit Euler discretization of an Ordinary Differential Equation (ODE).
LSAR: Efficient Leverage Score Sampling Algorithm for the Analysis of Big Time Series Data
We first develop a new fast algorithm to estimate the leverage scores of an autoregressive (AR) model in big data regimes.
HAWQ-V2: Hessian Aware trace-Weighted Quantization of Neural Networks
However, the search space for a mixed-precision quantization is exponential in the number of layers.
Limit theorems for out-of-sample extensions of the adjacency and Laplacian spectral embeddings
In both cases, we prove that when the underlying graph is generated according to a latent space model called the random dot product graph, which includes the popular stochastic block model as a special case, an out-of-sample extension based on a least-squares objective obeys a central limit theorem about the true latent position of the out-of-sample vertex.
Q-BERT: Hessian Based Ultra Low Precision Quantization of BERT
In particular, we propose a new group-wise quantization scheme, and we use a Hessian based mix-precision method to compress the model further.
Geometric Rates of Convergence for Kernel-based Sampling Algorithms
The rate of convergence of weighted kernel herding (WKH) and sequential Bayesian quadrature (SBQ), two kernel-based sampling algorithms for estimating integrals with respect to some target probability measure, is investigated.
Statistical guarantees for local graph clustering
In this paper, we adopt a statistical perspective on local graph clustering, and we analyze the performance of the l1-regularized PageRank method~(Fountoulakis et.
Bayesian experimental design using regularized determinantal point processes
In experimental design, we are given $n$ vectors in $d$ dimensions, and our goal is to select $k\ll n$ of them to perform expensive measurements, e. g., to obtain labels/responses, for a linear regression task.
Residual Networks as Nonlinear Systems: Stability Analysis using Linearization
We regard pre-trained residual networks (ResNets) as nonlinear systems and use linearization, a common method used in the qualitative analysis of nonlinear systems, to understand the behavior of the networks under small perturbations of the input images.
Distributed estimation of the inverse Hessian by determinantal averaging
In distributed optimization and distributed numerical linear algebra, we often encounter an inversion bias: if we want to compute a quantity that depends on the inverse of a sum of distributed matrices, then the sum of the inverses does not equal the inverse of the sum.
Physics-informed Autoencoders for Lyapunov-stable Fluid Flow Prediction
In addition to providing high-profile successes in computer vision and natural language processing, neural networks also provide an emerging set of techniques for scientific problems.
Traditional and Heavy Tailed Self Regularization in Neural Network Models
Random Matrix Theory (RMT) is applied to analyze the weight matrices of Deep Neural Networks (DNNs), including both production quality, pre-trained models such as AlexNet and Inception, and smaller models trained from scratch, such as LeNet5 and a miniature-AlexNet.
JumpReLU: A Retrofit Defense Strategy for Adversarial Attacks
To complement these approaches, we propose a very simple and inexpensive strategy which can be used to ``retrofit'' a previously-trained network to improve its resilience to adversarial attacks.
OverSketched Newton: Fast Convex Optimization for Serverless Systems
Motivated by recent developments in serverless systems for large-scale computation as well as improvements in scalable randomized matrix algorithms, we develop OverSketched Newton, a randomized Hessian-based optimization algorithm to solve large-scale convex optimization problems in serverless systems.
Inefficiency of K-FAC for Large Batch Size Training
In stochastic optimization, using large batch sizes during training can leverage parallel resources to produce faster wall-clock training times per training epoch.
Shallow Neural Networks for Fluid Flow Reconstruction with Limited Sensors
In many applications, it is important to reconstruct a fluid flow field, or some other high-dimensional state, from limited measurements and limited data.
Minimax experimental design: Bridging the gap between statistical and worst-case approaches to least squares regression
In the process, we develop a new algorithm for a joint sampling distribution called volume sampling, and we propose a new i. i. d.
Traditional and Heavy-Tailed Self Regularization in Neural Network Models
Random Matrix Theory (RMT) is applied to analyze the weight matrices of Deep Neural Networks (DNNs), including both production quality, pre-trained models such as AlexNet and Inception, and smaller models trained from scratch, such as LeNet5 and a miniature-AlexNet.
Heavy-Tailed Universality Predicts Trends in Test Accuracies for Very Large Pre-Trained Deep Neural Networks
In this paper, we show how to use a new Theory of Heavy-Tailed Self-Regularization (HT-SR) to answer this.
On the Computational Inefficiency of Large Batch Sizes for Stochastic Gradient Descent
Increasing the mini-batch size for stochastic gradient descent offers significant opportunities to reduce wall-clock training time, but there are a variety of theoretical and systems challenges that impede the widespread success of this technique.
A Short Introduction to Local Graph Clustering Methods and Software
Scalability problems led to the development of local graph clustering algorithms that come with a variety of theoretical guarantees.
Social and Information Networks
Implicit Self-Regularization in Deep Neural Networks: Evidence from Random Matrix Theory and Implications for Learning
Random Matrix Theory (RMT) is applied to analyze weight matrices of Deep Neural Networks (DNNs), including both production quality, pre-trained models such as AlexNet and Inception, and smaller models trained from scratch, such as LeNet5 and a miniature-AlexNet.
Newton-MR: Inexact Newton Method With Minimum Residual Sub-problem Solver
We consider a variant of inexact Newton Method, called Newton-MR, in which the least-squares sub-problems are solved approximately using Minimum Residual method.
Newton-ADMM: A Distributed GPU-Accelerated Optimizer for Multiclass Classification Problems
First-order optimization methods, such as stochastic gradient descent (SGD) and its variants, are widely used in machine learning applications due to their simplicity and low per-iteration costs.
Error Estimation for Randomized Least-Squares Algorithms via the Bootstrap
As a more practical alternative, we propose a bootstrap method to compute a posteriori error estimates for randomized LS algorithms.
GPU Accelerated Sub-Sampled Newton's Method
In particular, in convex settings, we consider variants of classical Newton\textsf{'}s method in which the Hessian and/or the gradient are randomly sub-sampled.
Hessian-based Analysis of Large Batch Training and Robustness to Adversaries
Extensive experiments on multiple networks show that saddle-points are not the cause for generalization gap of large batch size training, and the results consistently show that large batch converges to points with noticeably higher Hessian spectrum.
Out-of-sample extension of graph adjacency spectral embedding
Many popular dimensionality reduction procedures have out-of-sample extensions, which allow a practitioner to apply a learned embedding to observations not seen in the initial training sample.
Lectures on Randomized Numerical Linear Algebra
This chapter is based on lectures on Randomized Numerical Linear Algebra from the 2016 Park City Mathematics Institute summer school on The Mathematics of Data.
Avoiding Synchronization in First-Order Methods for Sparse Convex Optimization
Parallel computing has played an important role in speeding up convex optimization methods for big data analytics and large-scale machine learning (ML).
A Berkeley View of Systems Challenges for AI
With the increasing commoditization of computer vision, speech recognition and machine translation systems and the widespread deployment of learning-based back-end technologies such as digital advertising and intelligent infrastructures, AI (Artificial Intelligence) has moved from research labs to production.
Rethinking generalization requires revisiting old ideas: statistical mechanics approaches and complex learning behavior
Using this model, we describe how a very simple application of ideas from the statistical mechanics theory of generalization provides a strong qualitative description of recently-observed empirical results regarding the inability of deep neural networks not to overfit training data, discontinuous learning and sharp transitions in the generalization properties of learning algorithms, etc.
LASAGNE: Locality And Structure Aware Graph Node Embedding
For larger graphs with flat NCPs that are strongly expander-like, existing methods lead to random walks that expand rapidly, touching many dissimilar nodes, thereby leading to lower-quality vector representations that are less useful for downstream tasks.
GIANT: Globally Improved Approximate Newton Method for Distributed Optimization
For distributed computing environment, we consider the empirical risk minimization problem and propose a distributed and communication-efficient Newton-type optimization method.
Second-Order Optimization for Non-Convex Machine Learning: An Empirical Study
While first-order optimization methods such as stochastic gradient descent (SGD) are popular in machine learning (ML), they come with well-known deficiencies, including relatively-slow convergence, sensitivity to the settings of hyper-parameters such as learning rate, stagnation at high training errors, and difficulty in escaping flat regions and saddle points.
Newton-Type Methods for Non-Convex Optimization Under Inexact Hessian Information
In this light, we consider the canonical problem of finite-sum minimization, provide appropriate uniform and non-uniform sub-sampling strategies to construct such Hessian approximations, and obtain optimal iteration complexity for the corresponding sub-sampled trust-region and cubic regularization methods.
A Bootstrap Method for Error Estimation in Randomized Matrix Multiplication
In recent years, randomized methods for numerical linear algebra have received growing interest as a general approach to large-scale problems.
Capacity Releasing Diffusion for Speed and Locality.
As an application, we use our CRD Process to develop an improved local algorithm for graph clustering.
Skip-Gram − Zipf + Uniform = Vector Additivity
An unexpected {``}side-effect{''} of such models is that their vectors often exhibit compositionality, i. e., \textit{adding}two word-vectors results in a vector that is only a small angle away from the vector of a word representing the semantic composite of the original words, e. g., {``}man{''} + {``}royal{''} = {``}king{''}.
Capacity Releasing Diffusion for Speed and Locality
Thus, our CRD Process is the first local graph clustering algorithm that is not subject to the well-known quadratic Cheeger barrier.
Scalable Kernel K-Means Clustering with Nystrom Approximation: Relative-Error Bounds
This work analyzes the application of this paradigm to kernel $k$-means clustering, and shows that applying the linear $k$-means clustering algorithm to $\frac{k}{\epsilon} (1 + o(1))$ features constructed using a so-called rank-restricted Nystr\"om approximation results in cluster assignments that satisfy a $1 + \epsilon$ approximation ratio in terms of the kernel $k$-means cost function, relative to the guarantee provided by the same algorithm without the use of the Nystr\"om method.
Union of Intersections (UoI) for Interpretable Data Driven Discovery and Prediction
The increasing size and complexity of scientific data could dramatically enhance discovery and prediction for basic scientific applications.
Sketched Ridge Regression: Optimization Perspective, Statistical Perspective, and Model Averaging
In particular, there is a bias-variance trade-off in sketched MRR that is not present in sketched LSR.
Feature-distributed sparse regression: a screen-and-clean approach
Most existing approaches to distributed sparse regression assume the data is partitioned by samples.
Mapping the Similarities of Spectra: Global and Locally-biased Approaches to SDSS Galaxy Data
This technique permits us to characterize empirically the natural variations in observed spectra data, and we illustrate how this approach can be used in an exploratory manner to highlight both large-scale global as well as small-scale local structure in Sloan Digital Sky Survey (SDSS) data.
Lecture Notes on Spectral Graph Methods
These are lecture notes that are based on the lectures from a class I taught on the topic of Spectral Graph Methods at UC Berkeley during the Spring 2015 semester.
Lecture Notes on Randomized Linear Algebra
These are lecture notes that are based on the lectures from a class I taught on the topic of Randomized Linear Algebra (RLA) at UC Berkeley during the Fall 2013 semester.
Matrix Factorization at Scale: a Comparison of Scientific Data Analytics in Spark and C+MPI Using Three Case Studies
We explore the trade-offs of performing linear algebra using Apache Spark, compared to traditional C and MPI implementations on HPC platforms.
Distributed, Parallel, and Cluster Computing G.1.3; C.2.4
Sub-sampled Newton Methods with Non-uniform Sampling
As second-order methods prove to be effective in finding the minimizer to a high-precision, in this work, we propose randomized Newton-type algorithms that exploit \textit{non-uniform} sub-sampling of $\{\nabla^2 f_i(w)\}_{i=1}^{n}$, as well as inexact updates, as means to reduce the computational complexity.
FLAG n' FLARE: Fast Linearly-Coupled Adaptive Gradient Methods
We consider first order gradient methods for effectively optimizing a composite objective in the form of a sum of smooth and, potentially, non-smooth functions.
Sub-Sampled Newton Methods I: Globally Convergent Algorithms
As a remedy, for all of our algorithms, we also give global convergence results for the case of inexact updates where such linear system is solved only approximately.
Sub-Sampled Newton Methods II: Local Convergence Rates
In such problems, sub-sampling as a way to reduce $n$ can offer great amount of computational efficiency.
Fast Randomized Kernel Ridge Regression with Statistical Guarantees
One approach to improving the running time of kernel-based methods is to build a small sketch of the kernel matrix and use it in lieu of the full matrix in the machine learning task of interest.
A Local Perspective on Community Structure in Multilayer Networks
The analysis of multilayer networks is among the most active areas of network science, and there are now several methods to detect dense "communities" of nodes in multilayer networks.
Social and Information Networks Probability Adaptation and Self-Organizing Systems Data Analysis, Statistics and Probability Physics and Society
Optimal Subsampling Approaches for Large Sample Linear Regression
For unweighted estimation algorithm, we show that its resulting subsample estimator is not consistent to the full sample OLS estimator.
Block Basis Factorization for Scalable Kernel Matrix Evaluation
Kernel methods are widespread in machine learning; however, they are limited by the quadratic complexity of the construction, application, and storage of kernel matrices.
Weighted SGD for $\ell_p$ Regression with Randomized Preconditioning
We aim to bridge the gap between these two methods in solving constrained overdetermined linear regression problems---e. g., $\ell_2$ and $\ell_1$ regression problems.
Implementing Randomized Matrix Algorithms in Parallel and Distributed Environments
and demonstrate that $\ell_1$ and $\ell_2$ regression problems can be solved to low, medium, or high precision in existing distributed systems on up to terabyte-sized data.
Fast Randomized Kernel Methods With Statistical Guarantees
By extending the notion of \emph{statistical leverage scores} to the setting of kernel ridge regression, our main statistical result is to identify an importance sampling distribution that reduces the size of the sketch (i. e., the required number of columns to be sampled) to the \emph{effective dimensionality} of the problem.
Random Laplace Feature Maps for Semigroup Kernels on Histograms
With the goal of accelerating the training and testing complexity of nonlinear kernel methods, several recent papers have proposed explicit embeddings of the input data into low-dimensional feature spaces, where fast linear methods can instead be used to generate approximate solutions.
Think Locally, Act Locally: The Detection of Small, Medium-Sized, and Large Communities in Large Networks
In this paper, we adopt a complementary perspective that "communities" are associated with bottlenecks of locally-biased dynamical processes that begin at seed sets of nodes, and we employ several different community-identification procedures (using diffusion-based and geodesic-based dynamics) to investigate community quality as a function of community size.
Social and Information Networks Disordered Systems and Neural Networks Combinatorics Adaptation and Self-Organizing Systems Physics and Society
A Statistical Perspective on Algorithmic Leveraging
A detailed empirical evaluation of existing leverage-based methods as well as these two new methods is carried out on both synthetic and real data sets.
Quantile Regression for Large-scale Applications
Our empirical evaluation illustrates that our algorithm is competitive with the best previous work on small to medium-sized problems, and that in addition it can be implemented in MapReduce-like environments and applied to terabyte-sized problems.
Semi-supervised Eigenvectors for Large-scale Locally-biased Learning
For example, one might be interested in the clustering structure of a data graph near a prespecified "seed set" of nodes, or one might be interested in finding partitions in an image that are near a prespecified "ground truth" set of pixels.
Revisiting the Nystrom Method for Improved Large-Scale Machine Learning
Our main results consist of an empirical evaluation of the performance quality and running time of sampling and projection methods on a diverse suite of SPSD matrices.
Semi-supervised Eigenvectors for Locally-biased Learning
In many applications, one has information, e. g., labels that are provided in a semi-supervised manner, about a specific target region of a large data set, and one wants to perform machine learning and data analysis tasks nearby that pre-specified target region.
The Fast Cauchy Transform and Faster Robust Linear Regression
We provide fast algorithms for overconstrained $\ell_p$ regression and related problems: for an $n\times d$ input matrix $A$ and vector $b\in\mathbb{R}^n$, in $O(nd\log n)$ time we reduce the problem $\min_{x\in\mathbb{R}^d} \|Ax-b\|_p$ to the same problem with input matrix $\tilde A$ of dimension $s \times d$ and corresponding $\tilde b$ of dimension $s\times 1$.
Regularized Laplacian Estimation and Fast Eigenvector Approximation
Conversely, it will imply that the solution to this regularized estimation problem can be computed very quickly by running, e. g., the fast diffusion-based PageRank procedure for computing an approximation to the first nontrivial eigenvector of the graph Laplacian.
Randomized Dimensionality Reduction for k-means Clustering
On the other hand, two provably accurate feature extraction methods for $k$-means clustering are known in the literature; one is based on random projections and the other is based on the singular value decomposition (SVD).
Randomized algorithms for matrices and data
This monograph will provide a detailed overview of recent work on the theory of randomized matrix algorithms as well as the application of those ideas to the solution of practical problems in large-scale data analysis.
Data Structures and Algorithms
CUR from a Sparse Optimization Viewpoint
The CUR decomposition provides an approximation of a matrix X that has low reconstruction error and that is sparse in the sense that the resulting approximation lies in the span of only a few columns of X.
Effective Resistances, Statistical Leverage, and Applications to Linear Equation Solving
Our first and main result is a simple algorithm to approximate the solution to a set of linear equations defined by a Laplacian (for a graph $G$ with $n$ nodes and $m \le n^2$ edges) constraint matrix.
Numerical Analysis
Unsupervised Feature Selection for the k-means Clustering Problem
We present a novel feature selection algorithm for the $k$-means clustering problem.
Community Structure in Large Networks: Natural Cluster Sizes and the Absence of Large Well-Defined Clusters
A large body of work has been devoted to defining and identifying clusters or communities in social and information networks.
Data Structures and Algorithms Data Analysis, Statistics and Probability Physics and Society
