Study efficient power iteration for tensor models, proving convergence under specific conditions.
problem Simultaneous alternating power iteration for fixed-order asymmetric rank-one spiked tensor models.
method Finite-iteration local theory, geometrically decaying transient, fixed-order multilinear noise event, warm-start mechanism.
result Convergence to the unique informative local fixed point under specific conditions.
We study distributed computing of the truncated singular value decomposition problem. We develop an algorithm that we call \texttt{LocalPower} for improving communication efficiency. Specifically, we uniformly partition the dataset among m nodes and alternate between multiple (precisely p) local power iterations an…
Sharp analysis of power iteration for tensor PCA, improving convergence and stopping criteria.
problem Analyzing the power iteration algorithm for tensor PCA to improve convergence and stopping criteria.
method Sharp bounds on the number of iterations, revealing a smaller algorithmic threshold, proposing a stopping criterion.
result Sharp bounds on the number of iterations required for power method to converge, revealing a smaller algorithmic threshold than previously conjectured.
Alternating Minimization is a widely used and empirically successful heuristic for matrix completion and related low-rank optimization problems. Theoretical guarantees for Alternating Minimization have been hard to come by and are still poorly understood. This is in part because the heuristic is iterative and non-conve…
This paper proposes an alternating back-propagation algorithm for learning the generator network model. The model is a non-linear generalization of factor analysis. In this model, the mapping from the continuous latent factors to the observed signal is parametrized by a convolutional neural network. The alternating bac…
FedPower improves eigenspace estimation privacy in federated learning.
problem Privacy breaches and communication challenges in federated eigenspace estimation.
method FedPower uses a power method with local power iterations and global aggregation, weighted by OPT, and adds Gaussian noise for privacy.
result FedPower provides convergence bounds and demonstrates effectiveness in experiments.
Paper refutes conjecture on tensor power iteration convergence in overcomplete models.
problem Understanding convergence of tensor power iteration in overcomplete random tensors.
method Analysis of tensor power iteration dynamics from random initialization.
result Polynomially many steps are necessary for convergence, refutes logarithmic conjecture.
Efficiently compress pretrained models using RSI for improved predictive accuracy.
problem Efficiently compressing large pretrained models for practical deployment.
method Randomized subspace iteration (RSI) for low-rank approximation of pretrained models.
result RSI achieves near-optimal approximation quality and outperforms RSVD in predictive accuracy.
Tensor CANDECOMP/PARAFAC (CP) decomposition has wide applications in statistical learning of latent variable models and in data mining. In this paper, we propose fast and randomized tensor CP decomposition algorithms based on sketching. We build on the idea of count sketches, but introduce many novel ideas which are un…
We propose a new method for robust PCA -- the task of recovering a low-rank matrix from sparse corruptions that are of unknown value and support. Our method involves alternating between projecting appropriate residuals onto the set of low-rank matrices, and the set of sparse matrices; each projection is {\em non-convex…
Contemporary power grids are being challenged by rapid voltage fluctuations that are caused by large-scale deployment of renewable generation, electric vehicles, and demand response programs. In this context, monitoring the grid's operating conditions in real time becomes increasingly critical. With the emergent large …
NumPyro is a lightweight library that provides an alternate NumPy backend to the Pyro probabilistic programming language with the same modeling interface, language primitives and effect handling abstractions. Effect handlers allow Pyro's modeling API to be extended to NumPyro despite its being built atop a fundamentall…
New method explains GNNs using power iteration clustering.
problem Mysterious mechanism of message passing in GNNs.
method Subspace power iteration clustering (SPIC) models.
result Message passing in GNNs can be understood through power iteration.
More and more processes governing our lives use in some part an automatic decision step, where -- based on a feature vector derived from an applicant -- an algorithm has the decision power over the final outcome. Here we present a simple idea which gives some of the power back to the applicant by providing her with alt…
Given a dataset and an existing clustering as input, alternative clustering aims to find an alternative partition. One of the state-of-the-art approaches is Kernel Dimension Alternative Clustering (KDAC). We propose a novel Iterative Spectral Method (ISM) that greatly improves the scalability of KDAC. Our algorithm is …
In this paper, we provide local and global convergence guarantees for recovering CP (Candecomp/Parafac) tensor decomposition. The main step of the proposed algorithm is a simple alternating rank-1 update which is the alternating version of the tensor power iteration adapted for asymmetric tensors. Local convergence g…
New method learns collective variables using autoencoders for molecular simulations.
problem Learning low-dimensional slow degrees of freedom (collective variables) for molecular simulations.
method Iterative method involving CV learning with autoencoders and reweighting scheme.
result Achieves convergence of learned collective variables.
Paper uses SC to estimate hidden interference for WSRM.
problem Maximizing sum-rate with hidden interfering sources.
method Synthetic control (SC) for estimating counterfactual interference in WMMSE.
result SC-WMMSE outperforms original WMMSE in convergence and objective.
The paper analyzes the variance of different shuffling methods in stochastic gradient descent.
problem Understanding the variance of different shuffling methods in stochastic gradient descent.
method Power spectral density analysis to study the noise sequences of stochastic gradients.
result The stationary variances of iterates decrease in the order of SGD, SGD-RR, and SGD-SO.
Due to massive amounts of data distributed across multiple locations, distributed machine learning has attracted a lot of research interests. Alternating Direction Method of Multipliers (ADMM) is a powerful method of designing distributed machine learning algorithm, whereby each agent computes over local datasets and e…
Eigendecomposition (ED) is widely used in deep networks. However, the backpropagation of its results tends to be numerically unstable, whether using ED directly or approximating it with the Power Iteration method, particularly when dealing with large matrices. While this can be mitigated by partitioning the data in sma…
Tensor CANDECOMP/PARAFAC (CP) decomposition is an important tool that solves a wide class of machine learning problems. Existing popular approaches recover components one by one, not necessarily in the order of larger components first. Recently developed simultaneous power method obtains only a high probability recover…
Testing independence is of significant interest in many important areas of large-scale inference. Using extreme-value form statistics to test against sparse alternatives and using quadratic form statistics to test against dense alternatives are two important testing procedures for high-dimensional independence. However…
New algorithm solves minimax games with linear constraints.
problem Nonconvex minimax games with coupled linear constraints.
method Primal-dual alternating proximal gradient (PDAPG) algorithm.
result Achieves ε-stationary solution within O(ε^(-2)) iterations for strongly concave settings.
Characterizes a specific type of neural network for alternating group equivariance.
problem Understanding and characterizing neural networks with alternating group equivariance.
method Characterization of all possible An-equivariant neural networks using tensor powers of Rn. result Found a basis of matrices for learnable, linear An-equivariant layer functions. Power iteration has been generalized to solve many interesting problems in machine learning and statistics. Despite its striking success, theoretical understanding of when and how such an algorithm enjoys good convergence property is limited. In this work, we introduce a new class of optimization problems called scale …
Nonparametric two sample testing deals with the question of consistently deciding if two distributions are different, given samples from both, without making any parametric assumptions about the form of the distributions. The current literature is split into two kinds of tests - those which are consistent without any a…
Fast algorithm recovers principal eigenvector from noisy matrices.
problem Recovering the first principal eigenvector from noisy positive semidefinite matrices.
method Cone projected power iteration algorithm.
result Achieves polynomial time complexity and small error for certain convex cones.
We present a novel analysis of the dynamics of tensor power iterations in the overcomplete regime where the tensor CP rank is larger than the input dimension. Finding the CP decomposition of an overcomplete tensor is NP-hard in general. We consider the case where the tensor components are randomly drawn, and show that …
Magnetic resonance imaging (MRI) is known to be a slow imaging modality and undersampling in k-space has been used to increase the imaging speed. However, image reconstruction from undersampled k-space data is an ill-posed inverse problem. Iterative algorithms based on compressed sensing have been used to address the i…
ParPIC clusters directed graphs using random walks and diffusion operators.
problem Challenges in vertex-level clustering for directed graphs due to edge directionality.
method Parametrized Power-Iteration Clustering (ParPIC) based on reversible random walks and diffusion operators.
result ParPIC achieves competitive clustering accuracy with improved scalability compared to spectral and teleportation-based methods.
AGD converges in polynomial iterations to optimal matrix factorization.
problem Matrix factorization optimization with alternating gradient descent.
method Alternating gradient descent with fixed step size, proving convergence in polynomial iterations.
result AGD reaches ε-optimal factorization in T iterations with high probability.
Principal component analysis (PCA) is one of the most powerful tools in machine learning. The simplest method for PCA, the power iteration, requires O(1/Δ) full-data passes to recover the principal component of a matrix with eigen-gap Δ. Lanczos, a significantly more complex method, achieves an accelerated…
We introduce a new routing algorithm for capsule networks, in which a child capsule is routed to a parent based only on agreement between the parent's state and the child's vote. The new mechanism 1) designs routing via inverted dot-product attention; 2) imposes Layer Normalization as normalization; and 3) replaces seq…
New algorithms solve complex minimax problems without needing derivatives.
problem Solving nonconvex-concave minimax problems efficiently.
method Zeroth-order alternating and proximal gradient algorithms.
result Iteration complexity and function value estimation bounds established.
Critical volatility triggers log-normal to power-law transitions in interconnected systems.
problem Understanding the transition from log-normal to power-law distributions in interconnected systems.
method Analyzing an infinite option-on-option chain model, deriving a critical volatility threshold.
result A critical volatility threshold of approximately 250.66% for unconditional cases, dropping to 125.3% with selective survival.
Study spectral learning for odeco tensors, addressing initialization bottlenecks.
problem Recovering orthogonally decomposable tensors under noise.
method Investigates perturbation bounds, non-convex optimization, and initialization strategies.
result Initialization is the main bottleneck for efficient algorithms.
Implicit models can match or exceed explicit models with more test-time compute.
problem Understanding the expressive power and scaling of implicit models.
method Nonparametric analysis of expressive power, mathematical characterization of implicit operators, and test-time scaling experiments.
result Implicit models can progressively express more complex mappings through iteration, matching a richer function class with test-time compute.
This chapter deals with decentralized learning algorithms for in-network processing of graph-valued data. A generic learning problem is formulated and recast into a separable form, which is iteratively minimized using the alternating-direction method of multipliers (ADMM) so as to gain the desired degree of paralleliza…
Efficiently estimates Cox model coefficients without sharing data.
problem Privacy and ownership concerns in multi-center biomedical studies.
method Communication-efficient iterative distributed algorithms for estimation and inference.
result Achieves convergence rate of full-sample estimator with minimal iterations.
This dissertation advances scalable Gaussian processes using iterative methods and pathwise conditioning.
problem The classical Gaussian process formulation is not scalable for large datasets and modern hardware.
method Combining iterative methods and pathwise conditioning to improve scalability.
result Significantly reduced memory requirements and facilitated application to larger datasets.
QAOA matches classical tensor power iteration in spiked tensor model recovery.
problem Statistical estimation in spiked tensor model with computational gap.
method Analysis of QAOA performance on spiked tensor model.
result QAOA weak recovery threshold matches tensor power iteration.
Principal component analysis (PCA) is recognised as a quintessential data analysis technique when it comes to describing linear relationships between the features of a dataset. However, the well-known sensitivity of PCA to non-Gaussian samples and/or outliers often makes it unreliable in practice. To this end, a robust…
SMPI recovers tensor spikes from noisy data with improved performance.
problem Recovering tensor spikes corrupted by Gaussian noise.
method Selective Multiple Power Iterations (SMPI) with polynomial random initializations and symmetrized tensor power iterations.
result SMPI outperforms existing algorithms and approaches theoretical optimal recovery.
Novel algorithm for Markov decision processes using rank-one approximation.
problem Solving planning and learning problems of Markov decision processes.
method Policy iteration with rank-one approximation of transition probability matrix.
result The proposed algorithm consistently outperforms first-order algorithms and their accelerated versions.
Due to the surprisingly good representation power of complex distributions, neural network (NN) classifiers are widely used in many tasks which include natural language processing, computer vision and cyber security. In recent works, people noticed the existence of adversarial examples. These adversarial examples break…
Enhances power of covariance matrix tests for high-dimensional data.
problem Testing large covariance matrices in high-dimensional data.
method Proposes a new Fisher's combined probability test for quadratic form and maximum form statistics.
result Boosts power against more general alternatives.
Innovative neural networks reduce memory usage for efficient, accurate segmentation.
problem Efficiently segmenting large graphs with limited memory.
method Iterative neural networks with loops and multiple outputs.
result State-of-the-art semantic segmentation results on demanding datasets.