In this paper, we propose a data collaboration analysis method for distributed datasets. The proposed method is a centralized machine learning while training datasets and models remain distributed over some institutions. Recently, data became large and distributed with decreasing costs of data collection. If we can cen…
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48 results for “distributional data analysis”
Paper proposes distributed sparse multicategory discriminant analysis for classification.
problem Sparse multicategory classification with distributed data.
method Convex formulation, distributed setting, invariant discriminant subspace recovery.
result Distributed sparse multicategory linear discriminant analysis performs as good as centralized version after a few rounds of communications.
Elliptically-Contoured Tensor-variate Distributions with Application to Improved Image Learningstat.ME
Improved image learning using elliptically contoured tensor-variate distributions.
problem Inadequate statistical analysis for tensor-valued data, especially with heavier or lighter tails.
method Developed a family of elliptically contoured tensor-variate distributions and derived their properties and procedures for estimation.
result Tensor-variate classification rules and tensor-on-tensor regression better predict and characterize data than TVN-based methods.
New robust discriminant analysis for non-Gaussian data.
problem Classical discriminant analysis struggles with non-Gaussian distributions and contaminated datasets.
method Each data point follows its own ES distribution with arbitrary scale, leading to robust classification.
result Maximum-likelihood estimation and classification are simple, fast, and robust.
Bayesian analysis reveals asymmetry in financial data.
problem Quantifying asymmetry in financial time series data.
method Bayesian approach, t-Test generalization, two data distribution models, sensitivity analysis.
result Statistical significance of gain/loss asymmetry amounts.
We present new findings in regard to data analysis in very high dimensional spaces. We use dimensionalities up to around one million. A particular benefit of Correspondence Analysis is its suitability for carrying out an orthonormal mapping, or scaling, of power law distributed data. Power law distributed data are foun…
The paper proves consistency of archetypal analysis for multivariate data.
problem Finding optimal archetype points for multivariate data.
method Uses convex polytope to summarize data, proving consistency under specific distribution assumptions.
result Archetype points converge to optimal solution under certain conditions.
The study tackles modeling high-frequency financial data using continuous distributions, finding them inadequate.
problem Challenges in modeling high-frequency integer price changes with continuous distributions.
method Proposed a modified maximum likelihood estimation procedure to account for the discreteness of high-frequency price changes.
result Traditional GARCH models are not suitable for high-frequency data due to the discreteness of price changes.
Develops a Riemannian archetypal analysis for interpretable non-linear data.
problem Limited performance of classical archetypal analysis on non-linear data.
method Riemannian geometry for data-driven pullback, geodesic convex combinations, convex relaxation followed by non-convex refinement.
result Combines interpretability of classical archetypal analysis with expressive power of modern non-linear models.
New binary AA methods improve on existing techniques.
problem Binary data limitations in AA methods.
method Proposed two optimization frameworks for binary AA.
result Superior performance on synthetic and real binary data.
This paper analyzes data-driven Newsvendor problems and finds a wide range of possible regrets.
problem Guessing the number drawn from an unknown distribution with asymmetric costs.
method Unified analysis using the notion of clustered distributions and new lower bounds.
result The entire spectrum of achievable regrets from to is possible.
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.
A new robust and flexible classification method for non-Gaussian data.
problem Robustness to scale changes and non-Gaussian distributions in classical discriminant analysis.
method FEMDA uses arbitrary Elliptically Symmetrical distributions and scale parameters for each data point.
result FEMDA is robust to scale changes and outperforms other methods.
Prototypal analysis is introduced to overcome two shortcomings of archetypal analysis: its sensitivity to outliers and its non-locality, which reduces its applicability as a learning tool. Same as archetypal analysis, prototypal analysis finds prototypes through convex combination of the data points and approximates th…
This paper tackles distributed estimation of the top-L eigenspace in PCA for large data sets.
problem Challenges in estimating the top-L eigenspace in principal component analysis for large data sets.
method Proposes a novel multi-round algorithm using shift-and-invert preconditioning and convex optimization.
result Achieves a fast convergence rate and covers the targeted top-L eigenspace without explicit eigengap assumption.
Two derivations of PCA for distributional data.
problem PCA for datasets of distributions.
method Two derivations: variance maximization and reconstruction error minimization.
result Closed-form solution for distributional PCA.
An important part of the information gathering and data analysis is to find out what people think about, either a product or an entity. Twitter is an opinion rich social networking site. The posts or tweets from this data can be used for mining people's opinions. The recent surge of activity in this area can be attribu…
Proposes a robust factor analysis for matrix data.
problem Robust factor analysis for matrix data with heavy-tailed or contaminated data.
method Bilinear factor analysis based on the matrix-variate distribution.
result Significantly higher breakdown point than traditional methods.
The paper proposes a neural network model for estimating conditional mixture Weibull distributions with right-censored data.
problem Survival analysis with right-censored data in predictive maintenance and health fields.
method A neural network architecture is developed to estimate two-parameter Weibull distributions conditionally to features, extending to a finite mixture of Weibull distributions.
result The model outperforms state-of-the-art methods on real-world datasets and can consider any survival time horizon.
CROC identifies the earliest-changing stream as the root cause in multi-stream data.
problem Distribution-free root cause analysis in multi-stream data with unknown distributional changes.
method Conformal p-values and finite-sample valid confidence sets.
result CROC efficiently isolates the root cause under minimal assumptions.
Wasserstein archetypal analysis finds optimal data summaries using Wasserstein metric.
problem Finding optimal data summaries using Wasserstein metric.
method Alternative formulation of archetypal analysis based on Wasserstein metric, with regularization and gradient-based computational approach.
result Existence and consistency of solutions for the regularized problem.
Symbolic data analysis (SDA) is an emerging area of statistics concerned with understanding and modelling data that takes distributional form (i.e. symbols), such as random lists, intervals and histograms. It was developed under the premise that the statistical unit of interest is the symbol, and that inference is requ…
EDD uses entropy of distance distributions to cluster unlabeled data.
problem Challenges in clustering unlabeled high-dimensional data.
method EDD employs Shannon entropy to quantify distance distribution peaks.
result EDD detects varying degrees of clustering sensitivity.
Sharp analysis of out-of-distribution error in overparameterized models with importance weights.
problem Understanding and quantifying the degradation of performance in overparameterized models when faced with underrepresented data.
method Sharp analysis of an overparameterized Gaussian mixture model with spurious features and cost-sensitive interpolating solutions incorporating importance weights.
result Characterization of a novel tradeoff between worst-case robustness and average accuracy as a function of importance weight magnitude.
DCMA uses generative models to analyze treatment effects on entire outcome distributions.
problem Traditional mediation analysis focuses on summary contrasts, missing complex distributional changes.
method DCMA learns conditional generative models for mediators and outcome, reconstructing interventional distributions via Monte Carlo simulation.
result DCMA captures both summary effects and rich distributional contrasts like energy distance and Wasserstein distance.
DCMA uses generative models to analyze complex treatment effects on outcome distributions.
problem Analyzing complex and nonlinear causal mechanisms through outcome-level summary contrasts.
method Generative learning framework for identifying and estimating treatment effects on entire outcome distributions.
result Reconstructs interventional outcome distributions via Monte Carlo forward simulation, capturing both summary and distributional contrasts.
Canonical Correlation Analysis (CCA) is a classic technique for multi-view data analysis. To overcome the deficiency of linear correlation in practical multi-view learning tasks, various CCA variants were proposed to capture nonlinear dependency. However, it is non-trivial to have an in-principle understanding of these…
Paper improves stability analysis of SGD for various loss functions and data distributions.
problem Improving stability analysis of SGD for non-convex loss functions and data distributions.
method Analyzes stability of SGD for convex and non-convex loss functions, and improves data-dependent bounds.
result Improved stability bounds for non-convex loss functions and convex regularized loss functions.
New RESK distributions improve robust clustering of skewed data.
problem Robustly clustering non-symmetric, heavy-tailed data clusters.
method Proposes RESK distributions and an EM algorithm with robust skew-Huber M-estimator.
result Numerical experiments confirm the effectiveness of the proposed methods.
This paper reviews methods for distributed training of machine learning models from high-rate streams.
problem Training machine learning models from high-rate distributed streams in a compute- and bandwidth-limited setting.
method Recently developed methods for large-scale distributed stochastic optimization.
result There exist regimes where systems can learn from distributed, streaming data at order-optimal rates.
Unified analysis for deterministic samplers in diffusion models.
problem Challenges in analyzing deterministic samplers for diffusion models.
method Unified convergence analysis framework.
result Achieved polynomial iteration complexity for DDIM-type samplers.
UAPCA projects uncertain data to low dimensions using GMMs.
problem Uncertain multidimensional data not well described by normal distributions.
method Model data with Gaussian mixture models, derive UAPCA projection from general formulation.
result Low-dimensional projections better represent multidimensional distributions.
PGPCA improves PCA for nonlinear data in neuroscience.
problem Nonlinear data distribution in neuroscience.
method Developed PGPCA for nonlinear manifolds, incorporating EM algorithm.
result PGPCA outperforms PPCA in modeling data around nonlinear manifolds.
Big data sets must be carefully partitioned into statistically similar data subsets that can be used as representative samples for big data analysis tasks. In this paper, we propose the random sample partition (RSP) data model to represent a big data set as a set of non-overlapping data subsets, called RSP data blocks,…
Quantile normalisation is a popular normalisation method for data subject to unwanted variations such as images, speech, or genomic data. It applies a monotonic transformation to the feature values of each sample to ensure that after normalisation, they follow the same target distribution for each sample. Choosing a "g…
In this paper we perform a statistical analysis of the high-frequency returns of the IBEX35 Madrid stock exchange index. We find that its probability distribution seems to be stable over different time scales, a stylized fact observed in many different financial time series. However, an in-depth analysis of the data us…
Unified analysis of federated learning with compression for various data distributions.
problem Communication overhead in federated learning with unreliable or limited communication.
method Periodic compressed communication and local gradient tracking schemes.
result Sharp convergence rates for various objective functions and data distributions.
CEDA improves understanding of data fit to models.
problem Real-world data often deviates from theoretical models.
method Categorical Exploratory Data Analysis (CEDA) to highlight deviations.
result CEDA reveals where and how data fits or deviates from models.
Data describing historical economic growth are analysed. Included in the analysis is the world and regional economic growth. The analysis demonstrates that historical economic growth had a natural tendency to follow hyperbolic distributions. Parameters describing hyperbolic distributions have been determined. A search …
CDVI improves variational inference for survival analysis by considering censoring mechanisms.
problem Challenges in applying variational methods to survival data, especially the dependence on censoring.
method Censor-dependent variational inference (CDVI) tailored for latent variable models in survival analysis.
result Significant improvements in estimating individual survival distributions.
Firm size data usually do not show the normality that is often assumed in statistical analysis such as regression analysis. In this study we focus on two firm size data: the number of employees and sale. Those data deviate considerably from a normal distribution. To improve the normality of those data we transform them…
The paper addresses data uncertainty in graph embedding by modeling data points as Gaussian distributions.
problem Data uncertainty in machine learning pipelines leads to misleading embeddings and lower accuracy.
method The paper proposes modeling data uncertainty using Gaussian distributions and reformulates graph embedding techniques.
result The proposed methods improve the accuracy of graph embedding by accounting for data uncertainty.
We introduce a wrapped Gaussian for SPD matrices, enhancing data analysis.
problem Handling circular and non-flat data distributions on SPD manifolds.
method Introduced a non-isotropic wrapped Gaussian using the exponential map, derived theoretical properties, and proposed a maximum likelihood framework.
result Demonstrated the robustness and flexibility of the wrapped Gaussian model on synthetic and real-world datasets.
New models for analyzing microbiome data with interactions.
problem Analyzing compositional data with interactions.
method Exponential family models with generalized score matching.
result Effective estimation methods for compositional data with interactions.
Generative Adversarial Net (GAN) has been proven to be a powerful machine learning tool in image data analysis and generation. In this paper, we propose to use Conditional Generative Adversarial Net (CGAN) to learn and simulate time series data. The conditions can be both categorical and continuous variables containing…
Mixture of Experts (MoE) is a popular framework in the fields of statistics and machine learning for modeling heterogeneity in data for regression, classification and clustering. MoE for continuous data are usually based on the normal distribution. However, it is known that for data with asymmetric behavior, heavy tail…
In this dissertation we propose alternative analysis of distributed stochastic gradient descent (SGD) algorithms that rely on spectral properties of the data covariance. As a consequence we can relate questions pertaining to speedups and convergence rates for distributed SGD to the data distribution instead of the regu…
New tree splitting criteria improve probabilistic predictions.
problem Improving tree-based nonparametric predictive distributions.
method Using proper scoring rules for tree splitting criteria.
result Trees with new splitting criteria produce better predictive distributions.