The book explores alternatives to worst-case analysis for algorithm performance.
problem Providing strong worst-case guarantees for many algorithms is impossible.
method Surveying and detailing various nuanced analysis approaches.
result More nuanced analysis approaches are needed for fundamental problems.
Efficient private matrix analysis algorithms for recent variants.
problem Private analysis of recent matrix updates.
method Identifying sufficient conditions on positive semidefinite matrices.
result First efficient differentially private algorithms for various matrix analysis tasks.
Can textual data be compressed intelligently without losing accuracy in evaluating sentiment? In this study, we propose a novel evolutionary compression algorithm, PARSEC (PARts-of-Speech for sEntiment Compression), which makes use of Parts-of-Speech tags to compress text in a way that sacrifices minimal classification…
Improved analysis of UCBVI algorithm with better empirical performance.
problem Improving the UCBVI algorithm's performance and understanding its bounds.
method Refined analysis of UCBVI algorithm with improved bonus terms and regret analysis.
result Improving multiplicative constants in UCBVI bounds enhances empirical performance.
The paper analyzes GTD algorithms with finite-sample bounds.
problem Convergence rate analysis of GTD family of algorithms.
method Formulated as stochastic gradient algorithms and analyzed using saddle-point error.
result Obtained finite-sample bounds on GTD performance.
The paper sets limits for sequential prediction and recursive algorithms using entropy analysis.
problem Fundamental limitations in sequential prediction and recursive algorithms.
method Entropic analysis to investigate underlying relationships of data and noises.
result Derives Lp bounds quantifiable in conditional entropy. New algorithms for latent class analysis using regularized spectral clustering.
problem Identifying latent classes within populations from categorical data.
method Developed two new algorithms using a regularized Laplacian matrix to estimate latent classes.
result Our algorithms provide consistent latent class analysis under mild conditions and can accurately infer the number of latent classes.
Study on randomized algorithms for optimal stopping problems.
problem Optimal stopping problems in randomized algorithms.
method Forward and backward Monte Carlo based optimisation algorithms.
result Proved convergence of the proposed algorithms and derived convergence rates.
Refined analysis of Mitra's algorithm for discrete mixtures.
problem Classifying general discrete mixture distribution models.
method Spectral clustering tailored to bipartite stochastic block models.
result Improved separation conditions for probability distributions.
Bayesian nonparametrics are a class of probabilistic models in which the model size is inferred from data. A recently developed methodology in this field is small-variance asymptotic analysis, a mathematical technique for deriving learning algorithms that capture much of the flexibility of Bayesian nonparametric infere…
New framework for Adam-type algorithms with constant β1, improving regret analysis.
problem Theoretical vs. practical use of Adam and variants with constant β1.
method Proposed a novel framework to derive optimal, data-dependent regret bounds with constant β1.
result Optimal, data-dependent regret bounds with constant β1 are achievable without further assumptions.
Paper analyzes Greedy-GQ for reinforcement learning with Markovian noise.
problem Analyzing Greedy-GQ for reinforcement learning with Markovian noise.
method Develops finite-sample analysis for Greedy-GQ with linear function approximation under Markovian noise.
result Provides theoretical justification for choosing stepsizes for faster convergence.
We apply information-based complexity analysis to support vector machine (SVM) algorithms, with the goal of a comprehensive continuous algorithmic analysis of such algorithms. This involves complexity measures in which some higher order operations (e.g., certain optimizations) are considered primitive for the purposes …
Paper analyzes convergence of proximal algorithm in metric spaces without geodesic convexity.
problem Analyzing convergence of proximal algorithm in general metric spaces.
method Analysis of the Wasserstein proximal algorithm without geodesic convexity assumption.
result Establishes unbiased and linear convergence rate for proximal algorithm under natural Wasserstein inequality.
We apply the hybrid Monte Carlo (HMC) algorithm to the financial time sires analysis of the stochastic volatility (SV) model for the first time. The HMC algorithm is used for the Markov chain Monte Carlo (MCMC) update of volatility variables of the SV model in the Bayesian inference. We compute parameters of the SV mod…
Survey of de Casteljau's algorithm's applications in geometric data analysis.
problem No specific problem stated; focuses on algorithm applications.
method Constructive approach to generalize parametric smooth curves to manifolds.
result Algorithm provides principled way to analyze geometric data.
A new algorithm of the analysis of correlation among economy time series is proposed. The algorithm is based on the power law classification scheme (PLCS) followed by the analysis of the network on the percolation threshold (NPT). The algorithm was applied to the analysis of correlations among GDP per capita time serie…
Classification is an important supervised machine learning method, which is necessary and challenging issue for ecological research. It offers a way to classify a dataset into subsets that share common patterns. Notably, there are many classification algorithms to choose from, each making certain assumptions about the …
Sparsity-based models and techniques have been exploited in many signal processing and imaging applications. Data-driven methods based on dictionary and sparsifying transform learning enable learning rich image features from data, and can outperform analytical models. In particular, alternating optimization algorithms …
An online algorithm improves cPCA for efficient, interpretable data analysis.
problem Efficiently finding informative low-dimensional representations in large datasets.
method Developed an online algorithm for a modified cPCA* method.
result The online algorithm for cPCA* shows improved performance and interpretability.
Unified analysis of asynchronous-SGD algorithms for distributed learning.
problem Analyzing asynchronous-SGD in heterogeneous settings with varying speeds and data distributions.
method Unified convergence theory for non-convex smooth functions, including pure asynchronous SGD and its modifications.
result Unified convergence rates for various asynchronous algorithms, including novel methods.
Optimal analysis of subset-selection based L_p low rank approximation.
problem Finding a rank-k matrix X to minimize the entry-wise L_p loss of matrix A.
method Column subset selection algorithm with improved approximation ratio using Riesz-Thorin interpolation theorem.
result Improved approximation ratio for subset selection based L_p low rank approximation.
Large-scale L1-regularized loss minimization problems arise in high-dimensional applications such as compressed sensing and high-dimensional supervised learning, including classification and regression problems. High-performance algorithms and implementations are critical to efficiently solving these problems. Building…
SARSA is an on-policy algorithm to learn a Markov decision process policy in reinforcement learning. We investigate the SARSA algorithm with linear function approximation under the non-i.i.d.\ data, where a single sample trajectory is available. With a Lipschitz continuous policy improvement operator that is smooth eno…
Due to advances in sensors, growing large and complex medical image data have the ability to visualize the pathological change in the cellular or even the molecular level or anatomical changes in tissues and organs. As a consequence, the medical images have the potential to enhance diagnosis of disease, prediction of c…
Boosting improves ICA for better component recovery.
problem Improving ICA's reliance on prior knowledge of sources.
method Maximizing likelihood via boosting and fixed-point unmixing.
result Boosting-based ICA outperforms existing methods.
Study on optimal rates for sequential probability assignment using smoothed analysis.
problem Optimal rates for sequential probability assignment under smoothed adversaries.
method General-purpose reduction from minimax rates to transductive learning, development of an efficient algorithm using MLE oracle.
result Optimal (logarithmic) fast rates for parametric and finite VC dimension classes, sublinear regret for general classes.
This paper presents a stochastic behavior analysis of a kernel-based stochastic restricted-gradient descent method. The restricted gradient gives a steepest ascent direction within the so-called dictionary subspace. The analysis provides the transient and steady state performance in the mean squared error criterion. It…
The cumulant analysis plays an important role in non Gaussian distributed data analysis. The shares' prices returns are good example of such data. The purpose of this research is to develop the cumulant based algorithm and use it to determine eigenvectors that represent investment portfolios with low variability. Such …
New RL algorithms correct bias in dynamic data analysis.
problem Dynamic data generation and analysis create endogeneity issues.
method Instrument variable (IV)-based reinforcement learning (RL) algorithms.
result Established theoretical properties of IV-RL algorithms.
The paper analyzes Karcher means on restricted PSD matrices with statistical guarantees.
problem Statistical analysis of non-linear manifolds in machine learning.
method Intrinsic mean model on restricted PSD matrices, Karcher mean analysis, extrinsic signal-plus-noise model.
result Non-asymptotic statistical analysis of Karcher means with deterministic error bounds.
Run2Survive uses survival analysis for algorithm selection, outperforming traditional methods.
problem Handling censored runtime data in algorithm selection.
method Decision-theoretic approach leveraging survival analysis for censored data.
result Run2Survive outperforms state-of-the-art AS approaches in experiments.
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.
Regularizes ML algorithms for robust multivariate analysis against distribution shifts.
problem Ensuring robustness of multivariate analysis algorithms against distribution shifts.
method Integrates a causal regularisation term into the loss function of multivariate analysis algorithms.
result Demonstrates improved out-of-distribution generalisation with reduced-rank regression and partial least squares.
New analysis shows halting time is predictable for large models, improving optimization efficiency.
problem Understanding the average-case complexity of optimization algorithms for large-scale models.
method Average-case analysis of first-order methods on random least squares and neural networks.
result Halting time is independent of input distribution, leading to tighter convergence rates.
The regret bound of an optimization algorithms is one of the basic criteria for evaluating the performance of the given algorithm. By inspecting the differences between the regret bounds of traditional algorithms and adaptive one, we provide a guide for choosing an optimizer with respect to the given data set and the l…
New method simplifies data analysis.
problem Complex data analysis challenges.
method Innovative algorithm for data simplification.
result Significant reduction in analysis time.
This thesis analyzes and improves convergence rates of bilevel optimization algorithms in machine learning.
problem Convergence analysis and algorithm design for bilevel optimization in machine learning.
method Comprehensive convergence rate analysis for both problem-based and algorithm-based bilevel optimization formulations.
result First lower bounds and matching upper bounds for bilevel optimization, and new stochastic algorithms with lower complexity.
Improved analysis of accelerated noisy power method for PCA.
problem Inexact matrix-vector products in PCA settings.
method Improved analysis of Accelerated Noisy Power Method under milder perturbation conditions.
result Worst-case optimal convergence rate with relaxed noise conditions.
Analyzes deep neural networks training errors with SGD and random init.
problem Lack of rigorous understanding of deep learning algorithms.
method Mathematical analysis of deep learning with SGD and random init.
result First full error analysis for deep learning with SGD and random init.
Proposes EDM algorithm to accelerate model training in distributed networks.
problem Hindered effectiveness of distributed stochastic optimization algorithms due to data heterogeneity and network sparsity.
method Introduces Exact-Diffusion with Momentum (EDM) algorithm, incorporating momentum techniques to mitigate bias and enhance convergence rate.
result EDM algorithm converges sub-linearly to the optimal solution, radius independent of data heterogeneity, for non-convex objective functions.
This paper investigates asymptotic behaviors of gradient descent algorithms (particularly accelerated gradient descent and stochastic gradient descent) in the context of stochastic optimization arising in statistics and machine learning where objective functions are estimated from available data. We show that these alg…
Unified error analysis for low-rank approximation improves data assimilation performance.
problem Analyzing the error in low-rank approximation methods for data assimilation.
method Unified stochastic analysis framework for Frobenius norm error bounds on centered and non-standard Gaussian matrices.
result Unified bounds provide clearer interpretations and enable better practical choices for covariance matrices.
We analyze the convergence behaviour of a recently proposed algorithm for regularized estimation called Dual Augmented Lagrangian (DAL). Our analysis is based on a new interpretation of DAL as a proximal minimization algorithm. We theoretically show under some conditions that DAL converges super-linearly in a non-asymp…
Distance metric learning is a branch of machine learning that aims to learn distances from the data, which enhances the performance of similarity-based algorithms. This tutorial provides a theoretical background and foundations on this topic and a comprehensive experimental analysis of the most-known algorithms. We sta…
Paper analyzes how unlabeled data improves SSL and adversarial robustness.
problem Understanding how unlabeled data impacts SSL and adversarial robustness.
method Minimax analysis and adversarial training.
result Reconstruction-based SSL algorithm is rate-optimal under various models and enhances adversarial robustness.
This paper uses dynamical systems to analyze and ensure convergence of the Bayesian EM algorithm.
problem Ensuring convergence of the Bayesian EM algorithm in incomplete-data scenarios.
method Applying Lyapunov stability theory to discrete-time dynamical systems.
result Conditions for convergence and potential for fast convergence of MAP-EM are established.
Introduces geometric formulation of EM algorithm for robust inference and various applications.
problem Statistical inference with missing data or unobservables.
method Information geometric formulation of EM algorithm and its extensions.
result Outlier-robust inference algorithm and various applications in deep learning.