Paper proposes diagnostics for error and variance estimation in randomized matrix computations.
problem Safe use of randomized matrix algorithms in applications.
method Leave-one-out error estimator and jackknife resampling method.
result Provides rapid diagnostics to assess quality of randomized matrix computations.
New method optimizes hyperparameters for randomized algorithms like random feature regression.
problem Optimizing hyperparameters in randomized algorithms is challenging due to their stochastic nature.
method Introduced a random objective function and used ensemble Kalman inversion (EKI) for gradient-free optimization.
result Demonstrated successful optimization of hyperparameters in various randomized algorithms.
We propose accelerated randomized coordinate descent algorithms for stochastic optimization and online learning. Our algorithms have significantly less per-iteration complexity than the known accelerated gradient algorithms. The proposed algorithms for online learning have better regret performance than the known rando…
New random forest algorithm improves regression with missing data.
problem Regression with missing data values.
method New random forest algorithm compared to existing techniques.
result Improved performance in quadratic errors and bias compared to existing methods.
Improved matrix approximation using randomized algorithms.
problem Finding better approximations of given matrices.
method Randomized algorithms to compute (HT) as an improved approximation. result Computed (HT) provides a better approximation than given F∗. This study examines how randomness affects machine learning model performance.
problem The impact of randomness on machine learning model performance.
method Empirical study comparing randomness in model training and dataset partitioning.
result Randomness in model training causes more variation in FFNNs than tree-based methods.
HD algorithm simulates dynamics on random matrix ensembles without generating full matrices.
problem Simulating dynamics on dense random matrix ensembles with high space and time complexity.
method Householder reflectors for adaptive and recursive construction, deferring decisions.
result Significant reductions in runtime and memory footprint for practical T≪n. New MBQC algorithm uses randomness for generative modeling.
problem Designing efficient quantum algorithms for generative modeling.
method Proposes a variational MBQC algorithm that treats randomness as a resource.
result Randomness in MBQC can lead to significant gains in generative modeling performance.
Polynomial-time algorithm estimates edge density of random graphs with privacy and robustness.
problem Estimating edge density of random graphs while maintaining privacy and robustness.
method Sum-of-squares algorithm for robust edge density estimation and reduction from privacy to robustness.
result Optimal error rate up to logarithmic factors, matching theoretical lower bounds.
Gradient span algorithms show consistent progress in high dimensions.
problem Understanding consistent training progress in large machine learning models.
method Proving deterministic behavior of gradient span algorithms on Gaussian random functions.
result Gradient span algorithms have asymptotically deterministic behavior in high dimensions.
Despite widespread interest and practical use, the theoretical properties of random forests are still not well understood. In this paper we contribute to this understanding in two ways. We present a new theoretically tractable variant of random regression forests and prove that our algorithm is consistent. We also prov…
New algorithm learns random neural networks efficiently.
problem Learning random constant-depth neural networks efficiently.
method Presented a PTAS (Polynomial-Time Approximation Scheme) for learning random Xavier networks of fixed depth.
result For any fixed ε and depth i, there is a poly-time algorithm that learns random Xavier networks up to an additive error of ε.
Although the methods of bagging and random forests are some of the most widely used prediction methods, relatively little is known about their algorithmic convergence. In particular, there are not many theoretical guarantees for deciding when an ensemble is "large enough" --- so that its accuracy is close to that of an…
Spectral clustering has been one of the widely used methods for community detection in networks. However, large-scale networks bring computational challenges to the eigenvalue decomposition therein. In this paper, we study the spectral clustering using randomized sketching algorithms from a statistical perspective, whe…
Paper reinterprets ARP algorithm and improves its analysis and speed.
problem Column subset selection in data analysis.
method Volume sampling and active learning connections, new analysis, rejection sampling.
result Faster implementations and new analysis for ARP algorithm.
We propose a novel probabilistic method for detection of objects in noisy images. The method uses results from percolation and random graph theories. We present an algorithm that allows to detect objects of unknown shapes in the presence of random noise. The algorithm has linear complexity and exponential accuracy and …
Randomized SINDy learns dynamic data structures using probabilistic methods.
problem Learning time-dependent data structures in dynamic systems.
method Sequential machine learning with a probabilistic approach, incorporating feature augmentation and Tikhonov regularization.
result Demonstrated effectiveness in regression and binary classification using real-world data.
Randomized algorithm solves vector-valued regression problems with low-rank operators.
problem Vector-valued regression problems involving infinite-dimensional spaces.
method Randomized Reduced Rank Regression (R4) using Gaussian sketching for optimization.
result R4 estimators are efficient and accurate, with empirical risk close to optimal.
We consider statistical and algorithmic aspects of solving large-scale least-squares (LS) problems using randomized sketching algorithms. Prior results show that, from an \emph{algorithmic perspective}, when using sketching matrices constructed from random projections and leverage-score sampling, if the number of sampl…
Two ANOVA-based algorithms boost random Fourier feature models for function approximation.
problem Approximating high-dimensional functions with low-order interactions.
method Utilizes ANOVA decomposition to learn low-order functions and index sets of important variables.
result Significantly reduces approximation error compared to existing methods.
In this paper we study randomized optimal stopping problems and consider corresponding forward and backward Monte Carlo based optimisation algorithms. In particular we prove the convergence of the proposed algorithms and derive the corresponding convergence rates.
The paper improves bandit algorithms by incorporating random-effect models.
problem Improving statistical efficiency in multi-armed bandit problems with misspecified priors.
method Introduces a random-effect model to bandits, estimating arm means and designing a UCB algorithm ReUCB.
result Derives an upper bound on the Bayes regret of ReUCB, showing improved performance over Thompson sampling.
A new algorithm speeds up CP decomposition for large tensors.
problem Efficiently processing large-scale tensors in real-time.
method Randomized online CP decomposition (ROCP) algorithm.
result ROCP reduces computing time and memory usage significantly.
Paper explores grafting consistent estimators to improve Random Forest consistency.
problem Ensuring Random Forests are consistent despite their performance.
method Grafting consistent estimators onto a shallow CART.
result Grafted estimators provide a consistency guarantee and perform well empirically.
Optimal algorithms for online convex optimization with random order.
problem Online convex optimization with random order and non-convex loss functions.
method Stochastic gradient descent and algorithmic stability analysis.
result Achieves optimal bounds and significantly outperforms previous methods.
Survey on random features for kernel approximation, focusing on algorithms, theory, and practical applications.
problem Efficiently approximating kernel methods for large-scale problems.
method Random features techniques to speed up kernel methods.
result Need for a high number of random features for good approximation quality.
New framework reduces private mean estimation error with optimal efficiency.
problem Locally private mean estimation of high-dimensional vectors.
method ProjUnit framework: random projections, normalization, and optimal algorithm execution in lower dimensions.
result Optimal error up to a 1+o(1)-factor with computational efficiency and low communication complexity.
Paper proposes a fair grading method for randomized exams.
problem Ensuring fairness in grading for randomized exams.
method Maximum-likelihood estimator for Bradley-Terry-Luce model on student-question graph.
result Maximum-likelihood estimator is consistent and outperforms simple averaging in fairness and accuracy.
Transforms offline algorithms to online with low regret in random order model.
problem Developing online algorithms with low approximate regret from offline approximation algorithms.
method General reduction theorem and coreset construction method.
result Achieves polylogarithmic ε-approximate regret for various online problems.
A stability metric compares feature selection algorithms in machine learning.
problem Stability of feature selection algorithms in machine learning.
method Rank-based instability index to compare MDA, LIME, and SHAP algorithms.
result LIME and SHAP are more stable than MDA, with LIME being best for human interpretability.
Quantum algorithm speeds up learning from big data exponentially.
problem Scalable learning from big data with optimized random features.
method Quantum algorithm for sampling optimized random features.
result Exponential speedup in runtime compared to classical algorithms.
Polynomial-time algorithm matches correlated random graphs with non-vanishing correlation.
problem Matching correlated random graphs with non-vanishing edge correlation.
method Iterative algorithm for polynomial-time recovery of latent matching.
result Algorithm succeeds in recovering latent matching as long as edge correlation is non-vanishing.
Kernel ridgeless regression with random features shows good generalization without explicit regularization.
problem Generalization of kernel ridgeless regression without explicit regularization.
method Investigation of ridgeless regression with random features and stochastic gradient descent, exploring the effect of random features error and spectral density optimization.
result Random features error exhibits the double-descent curve, leading to improved generalization.
New random forest algorithms for PU learning minimize risk directly.
problem Learning from positive and unlabeled data.
method Recursive greedy risk minimization for decision trees.
result Efficient PU random forest algorithm with robustness and low hyperparameter tuning.
In this paper, we face the problem of simulating discrete random variables with general and varying distributions in a scalable framework, where fully parallelizable operations should be preferred. The new paradigm is inspired by the context of discrete choice models. Compared to classical algorithms, we add paralleliz…
Enhances random forest consistency and introduces DMRF for improved performance.
problem Improving the consistency and efficiency of random forest algorithms.
method Strengthened proof methods and propose DMRF algorithm.
result DMRF achieves better theoretical and experimental performance than previous variants.
Several useful variance-reduced stochastic gradient algorithms, such as SVRG, SAGA, Finito, and SAG, have been proposed to minimize empirical risks with linear convergence properties to the exact minimizer. The existing convergence results assume uniform data sampling with replacement. However, it has been observed in …
The Kaczmarz algorithm is popular for iteratively solving an overdetermined system of linear equations. The traditional Kaczmarz algorithm can approximate the solution in few sweeps through the equations but a randomized version of the Kaczmarz algorithm was shown to converge exponentially and independent of number of …
Efficient algorithm approximates discrete random variables with minimal Kolmogorov distance.
problem Estimating the probability of missing deadlines in series-parallel schedules.
method An efficient algorithm that computes a random variable with minimal Kolmogorov distance to a given discrete random variable.
result The algorithm efficiently approximates the probability of missing deadlines with minimal Kolmogorov distance.
This is a technical report which explores the estimation methodologies on hyper-parameters in Markov Random Field and Gaussian Hidden Markov Random Field. In first section, we briefly investigate a theoretical framework on Metropolis-Hastings algorithm. Next, by using MH algorithm, we simulate the data from Ising model…
The paper improves Kaczmarz algorithm with momentum for linear least squares.
problem Improving convergence of the Kaczmarz algorithm for linear least squares.
method Integrates geometrically smoothed momentum into the randomized Kaczmarz algorithm.
result Proves expected error reduction in singular vector directions.
RandNLA uses randomness for matrix problems in machine learning.
problem Matrix problems in machine learning.
method Randomized Numerical Linear Algebra.
result New challenges in RandNLA due to hardware trends and advances in ML.
Recursive stochastic algorithms have gained significant attention in the recent past due to data driven applications. Examples include stochastic gradient descent for solving large-scale optimization problems and empirical dynamic programming algorithms for solving Markov decision problems. These recursive stochastic a…
Algorithm solves job acceptance problem with random arrivals and values.
problem Decision-making under random job arrivals and values with limited acceptance.
method Proposes Non-Parametric Sequential Allocation (NPSA) algorithm.
result Expected reward converges to optimality as sample size increases.
Generalizes randomized SVD for better matrix approximations using Gaussian vectors.
problem Computing accurate rank-k approximations of matrices with limited data.
method Extends randomized SVD to multivariate Gaussian vectors, incorporating prior knowledge and using Gaussian processes.
result Demonstrates improved accuracy in approximating matrices and Hilbert-Schmidt operators.
Paper presents a randomized algorithm for SPCA with high probability approximation.
problem Sparse Principal Component Analysis (SPCA) is NP-hard.
method Based on basic SDP relaxation, the algorithm constructs deterministic and randomized solutions.
result The algorithm achieves an approximation ratio of at most the sparsity constant with high probability.
New stochastic gradient descent with random search directions improves efficiency and convergence.
problem Efficiency and convergence of stochastic gradient descent methods.
method Developed a new class of stochastic gradient descent algorithms with random search directions.
result Established almost sure convergence and provided Lp rates of convergence. New spectral algorithm estimates random graph parameters robustly against corrupted nodes.
problem Estimating the parameter of an Erdős-Rényi random graph with adversarial corruption.
method Spectral algorithm designed for computational efficiency, with an inefficient but information-theoretic alternative.
result Achieves optimal error rate up to logarithmic factors, matching statistical lower bounds.