K-means fails catastrophically in high dimensions, Hartigan's avoids it.
problem K-means algorithm's failure in high-dimensional data.
method Proof of k-means failure and Hartigan's algorithm success.
result Hartigan's algorithm avoids the catastrophic failure of k-means in high dimensions.
Hierarchical clustering is a popular method for analyzing data which associates a tree to a dataset. Hartigan consistency has been used extensively as a framework to analyze such clustering algorithms from a statistical point of view. Still, as we show in the paper, a tree which is Hartigan consistent with a given dens…
Kernel k-Groups uses Hartigan's method for clustering in metric spaces of negative type.
problem Clustering in metric spaces of negative type.
method Weighted energy statistics, quadratically constrained quadratic program, kernel k-groups, Hartigan's method.
result Improved performance in higher dimensions compared to spectral clustering and kernel k-means.
The paper connects two clustering methods by showing gradient ascent flow can move up the cluster tree.
problem Establishing a strong correspondence between clustering methods.
method Moving up the cluster tree by following the gradient ascent flow.
result Gradient ascent flow can be used to move up the cluster tree.
Defines hierarchical clustering axioms for various densities.
problem Defining hierarchical clustering for different types of densities.
method An axiomatic approach to piecewise constant densities, then extending to general densities.
result Our axiomatic definition results in Hartigan's cluster tree under certain conditions.
Finding the optimal k-means clustering is NP-hard in general and many heuristics have been designed for minimizing monotonically the k-means objective. We first show how to extend Lloyd's batched relocation heuristic and Hartigan's single-point relocation heuristic to take into account empty-cluster and single-poin…
A new fuzzy clustering method using hyperbolic smoothing for large datasets.
problem Building fuzzy clusters for large data sets efficiently.
method A novel smoothing numerical approach to relax the sum-of-squares criterion, converting the problem into a differentiable optimization problem.
result The method produces better fuzzy partitions compared to traditional fuzzy C-means. SCAMP clusters data by selecting candidate clusters that follow shape constraints, avoiding the need for tuning parameters.
problem Clustering data in high-dimensional space with unknown number of clusters.
method SCAMP formulates clustering as a search and selection problem, using shape constraints and preference functions to select clusters.
result SCAMP can be run multiple times to assess clustering uncertainty, providing a robust method for data annotation.
New methods improve clustering accuracy in noisy data sets.
problem Improving clustering accuracy in data sets with noise features.
method Feature rescaling factors to enhance clustering validity indexes.
result Our methods increase the likelihood of estimating the true number of clusters.
SparseMix clusters sparse high dimensional binary data efficiently.
problem Clustering sparse high dimensional binary data.
method SparseMix is a mixture model designed for sparse data, using an on-line Hartigan optimization algorithm.
result SparseMix builds partitions with higher compatibility with reference grouping than related methods.
Following Hartigan, a cluster is defined as a connected component of the t-level set of the underlying density, i.e., the set of points for which the density is greater than t. A clustering algorithm which combines a density estimate with spectral clustering techniques is proposed. Our algorithm is composed of two step…
Unified theory for estimating and completing matrices with biclustering structures.
problem Estimating and completing matrices with biclustering structures in partially observed and noisy data.
method Developed a constrained least squares estimator achieving minimax rate-optimal performance.
result Unified high probability upper bounds and matching minimax lower bounds for various scenarios.
The level set tree approach of Hartigan (1975) provides a probabilistically based and highly interpretable encoding of the clustering behavior of a dataset. By representing the hierarchy of data modes as a dendrogram of the level sets of a density estimator, this approach offers many advantages for exploratory analysis…
We describe k-MLE, a fast and efficient local search algorithm for learning finite statistical mixtures of exponential families such as Gaussian mixture models. Mixture models are traditionally learned using the expectation-maximization (EM) soft clustering technique that monotonically increases the incomplete (expec…
Improved iterative methods for risk parity portfolio weights.
problem Solving for portfolio weights in risk parity allocation.
method Enhanced CCD and Newton methods, including a rescaling step and improved initial guess.
result Improved CCD method is the best, three times faster with 40% fewer iterations.
Paper introduces stochastic mesh methods for efficient CVA computation.
problem Efficient computation of CVA for large systems using Monte Carlo methods.
method Introduces two stochastic mesh methods for CVA computation.
result Demonstrates the rate of convergence of the methods to real CVA values.
A new method combines Laplace and Variational Bayes for scalable inference.
problem Complex models and large datasets make exact inference infeasible.
method Low-Rank Variational Bayes Correction (VBC) using Laplace method and Variational Bayes correction in a lower dimension.
result The method ensures scalability in both model complexity and data size.
Unified framework for model explanation methods based on feature removal.
problem Unclear relationships and preferences among various model explanation methods.
method Characterizes removal-based explanations along three dimensions.
result Unified 26 existing methods, including widely used approaches.
A new method speeds up optimization for sums, simpler than others.
problem Optimizing finite sums, especially in non-smooth cases.
method A novel accelerated method based on SAGA, with one parameter.
result Achieves accelerated convergence on strongly convex smooth problems.
Unified analysis of momentum methods for deep learning.
problem Convergence analysis of stochastic momentum methods for convex and non-convex optimization.
method Developed a convergence analysis for two stochastic momentum methods.
result Unified framework revealing similarities and differences between methods.
This work reviews and evaluates methods for predicting prediction intervals in regression problems.
problem Calibration of prediction intervals in regression problems.
method Four classes of methods: Bayesian, ensemble, direct interval estimation, and conformal prediction.
result Conformal prediction can be used as a general calibration procedure.
Derives kernel PCA with Nyström method for scalability.
problem Scalability of kernel PCA.
method Nyström method for kernel PCA.
result Provides scalable alternative to full kernel PCA.
Develops a fast method for pricing American options under variance gamma model.
problem Inefficient methods for pricing American options under variance gamma model.
method Inspired by quadratic approximation method, uses machine learning on pre-calculated quantities to reduce error.
result Proposed method is efficient and accurate for practical use.
Two RBF methods solve complex financial derivatives pricing problems.
problem Pricing derivatives in models with multiple stochastic factors.
method Radial Basis Function Partition of Unity and Radial Basis Function generated Finite Differences methods.
result Both methods achieve high accuracy and are efficient for solving multi-dimensional PDEs.
New method combines spectral and sparse methods for Gaussian processes.
problem Efficiently fitting Gaussian processes to large datasets.
method Orthogonally decoupled variational Fourier features.
result Competitive performance on synthetic and real-world data.
Simple stochastic Newton and cubic Newton methods with fast convergence.
problem Minimizing large numbers of smooth and strongly convex functions.
method Stochastic Newton and cubic Newton methods with simple local linear-quadratic rates.
result Local linear-quadratic convergence results with fast adaptation to problem's curvature.
Improved spectral methods of moments for robust latent variable model learning.
problem Limited robustness of spectral methods of moments to model misspecification.
method Hierarchical approach using approximate joint diagonalization instead of tensor decomposition.
result Our method outperforms previous tensor decomposition methods in speed and model quality.
VAN method optimizes learning tasks with unified methods.
problem Optimizing learning tasks in active and reinforcement learning.
method Variational Adaptive-Newton method that unifies optimization, inference, and evolution strategies.
result VAN performs well on various learning tasks.
A comprehensive benchmark of 15 scRNA-seq imputation methods across various datasets and analyses.
problem Imputation of single-cell RNA sequencing data to recover latent transcriptional signals.
method Evaluation of 15 imputation methods across 30 datasets and 6 downstream analyses.
result Traditional methods generally outperform DL-based methods in scRNA-seq data analysis.
New methods using natural gradient for structured optimization.
problem Structured optimization problems.
method Structured second-order methods via natural gradient descent.
result Efficiency demonstrated on non-convex and deep learning problems.
Improved A2C method with lower variance.
problem Reducing variance in deep policy gradient methods.
method Using control variate theory, derived a new A2C formulation with lower variance.
result New A2C method has lower variance and improved performance.
A new method speeds up deep neural network training.
problem Nonconvex optimization in deep neural networks.
method Scaled conjugate gradient method for nonconvex optimization.
result The method converges faster and achieves lower scores in practical applications.
We propose a new stochastic dual coordinate ascent technique that can be applied to a wide range of regularized learning problems. Our method is based on Alternating Direction Multiplier Method (ADMM) to deal with complex regularization functions such as structured regularizations. Although the original ADMM is a batch…
NCG methods improve shape optimization efficiency.
problem Shape optimization problems
method Nonlinear conjugate gradient methods
result NCG methods are efficient for shape optimization
Proposes UTC method for stock price prediction with uncertainty quantification.
problem Lack of uncertainty estimates in stock prediction methods.
method Combines TC method with probabilistic modeling for point and uncertainty predictions.
result UTC method achieves higher returns and lower risks than baselines.
Various approaches to gene selection for cancer classification based on microarray data can be found in the literature and they may be grouped into two categories: univariate methods and multivariate methods. Univariate methods look at each gene in the data in isolation from others. They measure the contribution of a p…
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.
Geometric methods study 3-manifold splittings.
problem Studying Heegaard splittings of 3-manifolds.
method Geometric approaches.
result Recent advances in geometric methods.
A novel weighted feature selection method using fuzzy sets improves classification accuracy and stability.
problem Improving feature selection accuracy and stability in machine learning models.
method Combination of four feature selection methods using fuzzy sets and bootstrap.
result Our method achieved significantly higher stability than individual methods.
New method improves accuracy in computing implied volatility.
problem Computing implied volatility from the Black-Scholes model.
method Adaptive gradient descent optimizers for numerical computation.
result More accurate results compared to close form approximation and Newton-Raphson method.
The paper examines Wiener process for LID estimation methods.
problem Estimating local intrinsic dimension in high-dimensional datasets.
method Investigates recent LID estimation methods from a Wiener process perspective.
result Explains how methods behave under non-ideal conditions.
Discuss ML methods for economists, highlighting better performance in econometrics.
problem Applying ML methods to econometrics problems.
method Supervised and unsupervised learning methods, matrix completion, causal inference, optimal policy estimation.
result ML methods often outperform traditional econometric methods in specific econometrics problems.
New method detects business-relevant outliers in e-commerce conversion rates.
problem Identifying outliers in e-commerce conversion rate data.
method A novel unsupervised fluid IQR method that adjusts sensitivity based on platform activity.
result Fluid IQR method outperforms existing methods in business-relevance and robustness.
Saliency methods often misattribute predictions due to input transformations.
problem Saliency methods lack reliability when explanations are sensitive to non-contributing factors.
method Used a simple pre-processing step to demonstrate that transformations with no effect on the model can cause misleading attributions.
result Saliency methods that do not satisfy input invariance (mirror model sensitivity to input transformations) result in misleading attributions.
The paper introduces admissible hierarchical clustering methods for asymmetric networks.
problem Characterizing and implementing hierarchical clustering methods for asymmetric networks.
method The paper characterizes admissible hierarchical clustering methods and proposes algorithms for their implementation.
result The paper describes three families of intermediate methods for admissible hierarchical clustering of asymmetric networks.
Medical image reconstruction advances from sparse models to machine learning.
problem Improving image quality and reducing noise in medical imaging.
method Iterative reconstruction, modified data acquisition methods, and machine learning models.
result Machine learning methods show promise in improving image quality.
We propose an optimization method for minimizing the finite sums of smooth convex functions. Our method incorporates an accelerated gradient descent (AGD) and a stochastic variance reduction gradient (SVRG) in a mini-batch setting. Unlike SVRG, our method can be directly applied to non-strongly and strongly convex prob…
R package for counterfactual explanation methods.
problem Lack of unified interfaces for counterfactual explanation methods.
method Developed a modular R6-based interface for three existing counterfactual methods and proposed extensions.
result Comparison of implemented methods' quality and runtime behavior.