Proposes a method to optimize class mean preservation in kernel-based feature spaces.
problem Optimizing the selection of kernel subspace for better performance.
method Component analysis method for kernel-based dimensionality reduction that optimally preserves class mean distances.
result Discriminant analysis version of the proposed method provides insights into feature space properties.
This study examines whether PCA can effectively identify nitrogen pollution sources in rivers.
problem Identifying pollution sources in rivers for effective environmental management.
method Principal Component Analysis and its modifications, along with Independent Component Analysis and Factor Analysis, are applied to nitrogen pollution source identification.
result PCA and related techniques can be powerful tools for uncovering nitrogen pollution sources in rivers.
Proposes a multivariate regression model for better analysis of multiple datasets.
problem Insufficient performance of single-dataset analysis in integrative studies.
method Sparse estimation for variable and group selection, alternating direction method of multipliers algorithm.
result Demonstrated improved performance through simulations and real data analysis.
Paper introduces probabilistic methods to approximate archetypal analysis, reducing complexity.
problem Inherent computational complexity of archetypal analysis limits its practical applicability.
method Two preprocessing techniques: dimensionality reduction and representation cardinality reduction, using probabilistic geometry.
result The method effectively reduces scaling and provides near-optimal solutions for prediction errors.
Interactive DR framework for comparing datasets.
problem Limited flexibility in existing DR methods for comparative analysis.
method Unified linear comparative analysis (ULCA) with interactive optimization and visualization.
result ULCA and optimization algorithm improve comparative analysis efficiency and flexibility.
Unified analysis of momentum methods in deep learning.
problem Theoretical analysis of convergence and generalization of stochastic momentum methods.
method Unified framework for analyzing SG, SHB, and SNAG methods; convergence rates and stability analysis.
result Momentum methods do not improve the training objective but enhance model stability and generalization.
Paper analyzes robust matrix completion with efficient nonconvex method and leave-one-out analysis.
problem Robust matrix completion with sparse noise.
method Alternates between projected gradient step for low-rank and thresholding step for sparse noise.
result Achieves linear convergence for general thresholding functions.
Unified analysis of stochastic gradient methods for convex and smooth optimization.
problem Minimizing composite convex and smooth functions.
method Unified convergence analysis of various stochastic gradient methods.
result Unified convergence rates for a variety of methods including proximal SGD, variance reduced methods, quantization, and coordinate descent.
Alternative wavelet analysis method for financial signals.
problem Analyzing oscillations in financial signals with noise.
method Modeling financial signals as isolated events producing ripples of various frequencies.
result Element analysis distinguishes between noise and logically matched generators.
In this dissertation, the main goal is visualisation of financial time series. We expect that visualisation of financial time series will be a useful auxiliary for technical analysis. Firstly, we review the technical analysis methods and test our trading rules, which are built by the essential concepts of technical ana…
Sobol method applied to probabilistic networks for sensitivity analysis.
problem Measuring influence of probabilistic network nodes on a quantity of interest.
method Transforms global sensitivity analysis into marginalization inference exploiting network structure.
result Efficient computation of sensitivity indices for complex networks.
A new robust scaling approach improves downstream metabolomics analysis.
problem Challenges in choosing scaling techniques for metabolomics data.
method Introduces a weighted scaling approach robust to outliers.
result The proposed method outperforms traditional scaling techniques in both outlier-free and outlier-present datasets.
A new method speeds up factor analysis for high-dimensional data.
problem Estimating covariance parameters in high-dimensional Gaussian data with limited observations.
method Matrix-free likelihood method using implicitly restarted Lanczos and limited-memory quasi-Newton algorithms.
result Our method is faster than EM without sacrificing accuracy.
Survey of spectral, probabilistic, and deep metric learning methods.
problem Developing effective distance metrics for various machine learning tasks.
method Divided into spectral, probabilistic, and deep approaches, covering various techniques and their applications.
result Comprehensive overview of metric learning methods, including new developments and applications.
Topological data analysis quantifies structural dynamics using persistent homology.
problem Analyzing the shape and topology of structural dynamics data.
method Topological Data Analysis (TDA) with persistent homology to quantify shape over scales.
result Persistent homology reveals significant changes in manifold shape due to damage, not temperature.
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.
New ICA method improves on existing techniques.
problem Finding independent components in data.
method Multiple-weighted Independent Component Analysis (MWeICA) based on approximate diagonalization of weighted covariance matrices.
result MWeICA achieves better results than state-of-the-art ICA methods with similar computational time.
A hierarchical approach improves classification accuracy in large datasets.
problem Improving classification accuracy in large datasets with high dimensionality.
method Hierarchical subspace learning to scale manifold learning methods.
result Average 5% increase in classification accuracy.
A new PMA method combines PCA and PLS for better classification.
problem Improving classification performance in data analysis.
method Combines PCA and PLS through multiple sub-PLS models and PCA on the joint coefficient matrix.
result The proposed PMA method achieves better classification performance and stability.
New method uses topological data analysis to study stock market crashes.
problem Characterizing and predicting stock market crashes.
method Topological data analysis, persistence landscape, dynamic time series analysis.
result Demonstrates effectiveness of new method for Flash Crash characterization and prediction.
The process of collecting and organizing sets of observations represents a common theme throughout the history of science. However, despite the ubiquity of scientists measuring, recording, and analyzing the dynamics of different processes, an extensive organization of scientific time-series data and analysis methods ha…
Explains gradient descent methods and their convergence, focusing on simple analysis.
problem Understanding and analyzing gradient descent methods and their variants.
method Elementary mathematical analysis focusing on structures and assumptions of objective functions.
result Unified convergence analysis of various gradient descent methods and variants.
Linear dimensionality reduction methods are a cornerstone of analyzing high dimensional data, due to their simple geometric interpretations and typically attractive computational properties. These methods capture many data features of interest, such as covariance, dynamical structure, correlation between data sets, inp…
New methods integrate nonlinear, sparse, and multi-view aspects for high-dimensional data analysis.
problem Integrating nonlinear dependence, sparsity, and multi-view data in high-dimensional datasets.
method Proposes HSIC-SGCCA, SA-KGCCA, and TS-KGCCA methods for multi-view high-dimensional data analysis.
result HSIC-SGCCA outperforms competing methods in multi-view variable selection.
This paper analyzes text in financial disclosures to improve financial analysis.
problem Insufficient analysis of unstructured text in financial disclosures.
method Reviews and explores methods in computational linguistics and NLP.
result Highlights limitations of sentiment metrics and suggests future research areas.
Survey article on solving geometric problems with calculus and harmonic analysis.
problem Solving geometric problems using functional calculus and harmonic analysis.
method Combining methods from functional calculus and real-variable harmonic analysis.
result Recent geometric problems have been resolved by these methods.
Paper combines geometry and time-series analysis for spatiotemporal data.
problem Multivariate time-series data from multiple sensors.
method Combines manifold learning, Riemannian geometry, and spectral analysis.
result Proposes Riemannian multi-resolution analysis (RMRA) for dynamic mode extraction.
Proposes counterfactual explainability for causal attribution, extending variance analysis methods.
problem Lack of mechanistic understanding in existing tools for explaining complex models.
method Extends global sensitivity analysis methods to causal explanations using directed acyclic graphs.
result Developed methods to estimate counterfactual explainability and applied to income inequality analysis.
This work connects LLE, factor analysis, and probabilistic PCA through a stochastic perspective.
problem Exploring the theoretical connection between LLE, factor analysis, and probabilistic PCA.
method Solving the stochastic linear reconstruction of LLE using expectation maximization.
result LLE, factor analysis, and probabilistic PCA are shown to be connected through a stochastic perspective.
iNNvestigate simplifies neural network analysis.
problem Understanding and analyzing complex neural networks is difficult.
method Provides a common interface and implementation for analysis methods.
result Demonstrates versatility in analyzing various neural network architectures.
Method quantifies sensitivity of reliability analysis to uncertainty sources.
problem Computational expense in reliability analysis of complex models.
method Gaussian process surrogate model, active learning, sensitivity analysis.
result Reduces main source of error in estimating rare event probabilities.
Proposes HGP to improve survival analysis models.
problem Improving survival analysis models by addressing density function changes.
method Imposes constraints on local data points by regularizing the hazard function gradient.
result HGP enhances survival analysis model performance.
ACA identifies and explains anomalies in data.
problem Explaining anomalies in non-supervised data analysis.
method Abnormal Component Analysis (ACA) using data depth.
result ACA provides a linear explanation for anomalies.
HACSurv models dependencies between competing risks and censoring for improved survival analysis.
problem Inaccurate survival predictions due to ignoring dependencies between competing risks and censoring.
method HACSurv uses hierarchical Archimedean copulas to model dependencies and cause-specific survival functions.
result HACSurv improves accuracy in survival predictions and captures complex risk interactions.
Paper relaxes factor analysis for noisy data, improving robustness.
problem Challenges in finding robust low dimensional approximations for data with heteroskedastic noise.
method Introduces a relaxed version of Minimum Trace Factor Analysis (MTFA) as a convex optimization method.
result Effective at not overfitting to heteroskedastic perturbations and addressing common issues in factor analysis.
Proposes a new method for high-dimensional data analysis.
problem Sparse PCA limitations in high-dimensional data analysis.
method Low-rank principal eigenmatrix analysis, matricized rank-truncated power method.
result Competitive empirical performance in synthetic data sets.
A new method for time series analysis that highlights important signals.
problem Finding signals that matter most in time series data.
method Contrastive Multivariate Singular Spectrum Analysis (CMSA) using a background dataset.
result CMSA identifies signals that are more relevant to the analyst than those with the highest variance.
Improved LDA method for better classification and dimensionality reduction.
problem Improving linear discriminant analysis for better classification performance.
method Integrates spectrally-corrected covariance matrix and regularized discriminant analysis.
result SRLDA has a linear classification global optimal solution under spiked model assumption.
Paper proposes a deep learning method to estimate fill probabilities of limit orders in LOBs.
problem Estimating the fill probabilities of limit orders in different levels of a limit order book.
method Survival analysis model using a convolutional-Transformer encoder and a monotonic neural network decoder.
result The proposed method significantly outperforms other approaches in survival analysis.
New method clusters travel behavior data from 1990-2017.
problem Challenges in analyzing large-scale travel data.
method Divide and Combine K-means clustering on time series data.
result Activity-travel patterns can be grouped into three clusters.
Method of moving planes used for proving symmetry in PDEs and geometric analysis.
problem Proving symmetry properties in PDEs and geometric analysis.
method Method of the moving planes for quantitative studies.
result Quantitative approximate symmetry results obtained.
Neural network learns kernel functions for survival analysis and prediction intervals.
problem Predicting survival times for individuals based on similar training subjects.
method Develops a neural network framework to learn kernel functions for kernel survival analysis and uses these to construct valid prediction intervals.
result Neural network survival estimators are competitive with existing methods and provide valid prediction intervals.
Genetic programming optimizes Gaussian kernels for better sentiment analysis.
problem Improving accuracy of sentiment analysis in text.
method Genetic Programming applied to evolve more effective Gaussian kernels.
result The evolved kernels outperform traditional Gaussian Processes in sentiment analysis.
This paper reviews methods for feature selection and extraction in pattern analysis.
problem Complex raw data require feature selection or extraction for better discrimination or representation.
method Reviews different methods of feature selection and extraction.
result Compares various methods of feature selection and extraction.
Paper proposes a method to preserve multimodal sentiment analysis fidelity.
problem Lack of fidelity in multimodal fusion for sentiment analysis.
method Variational autoencoder-based approach for modality fusion.
result Empirically shows superior performance over state-of-the-art methods.
We study the properties of memory of a financial time series adopting two different methods of analysis, the detrended fluctuation analysis (DFA) and the analysis of the power spectrum (PSA). The methods are applied on three time series: one of high-frequency returns, one of shuffled returns and one of absolute values …
Unified analysis of SGD variants for nonconvex federated optimization.
problem Performance of stochastic gradient methods in nonconvex optimization.
method Proposed a unified assumption for modeling stochastic gradient second moment, leading to a single convergence analysis for various methods.
result Unified convergence analysis for a wide range of SGD variants and distributed methods.
New method simplifies data analysis.
problem Complex data analysis challenges.
method Innovative algorithm for data simplification.
result Significant reduction in analysis time.