PPF uses projections to improve classification accuracy.
problem Improving classification accuracy in multi-class problems.
method PPF constructs trees using projections of variables, enhancing traditional random forest.
result PPF outperforms traditional random forest in multi-class problems.
Interactive graphics help diagnose forest classifiers in R.
problem Exploring and understanding complex ensemble models like random forests.
method Constructing and visualizing data interactively using R packages.
result Interactive graphics provide insights into model complexity and variable importance.
The paper compares PCA and PP for scRNA sequencing data.
problem Limitations of PCA in scRNA sequencing data.
method Applied PCA and PP (using negative Shannon's entropy) on scRNA sequencing data.
result PP outperforms PCA in scRNA sequencing data.
The paper finds non-Gaussian directions in high-dimensional data using Wasserstein distance.
problem Locating interesting non-Gaussian features in high-dimensional data.
method Projection pursuit using 2-Wasserstein distance to maximize the difference from Gaussian.
result Statistical guarantees for accurately approximating an unknown low-dimensional non-Gaussian subspace.
Enhances neural networks' explainability without sacrificing accuracy.
problem Lack of model interpretability in neural networks.
method Sparse additive subnetworks, projection pursuit with orthogonality constraint, smooth function approximation.
result Proposes an explainable neural network (xNN) with superior balance between prediction performance and interpretability.
Product models of low dimensional experts are a powerful way to avoid the curse of dimensionality. We present the ``under-complete product of experts' (UPoE), where each expert models a one dimensional projection of the data. The UPoE is fully tractable and may be interpreted as a parametric probabilistic model for pro…
Enhances projection pursuit tree classifier with visual diagnostics for better multi-class classification.
problem Rigidity of original algorithm limits performance in complex high-dimensional classification problems.
method Allowing more splits and flexible class groupings in projection pursuit computation, and developing visual diagnostics.
result Demonstrates enhanced classifier performs as intended through interactive visual diagnostics.
Paper proposes PPMM for fast estimation of large-scale OTM.
problem Estimation of large-scale optimal transport maps (OTM) is challenging due to the curse of dimensionality.
method Combines projection pursuit regression and sufficient dimension reduction to adaptively select projection directions.
result PPMM consistently estimates the most informative projection direction and weakly converges to the target OTM.
Paper proposes a novel approach to density ratio estimation using projection pursuit.
problem Density ratio estimation challenges in high dimensions and model misspecification.
method The approach uses projection pursuit to approximate density ratios, addressing high dimensionality and model flexibility issues.
result The proposed estimator is consistent and converges at a certain rate, outperforming existing methods in experiments.
A novel PP algorithm using GMMs and GAs for detecting informative structures.
problem Detecting informative structures in multivariate datasets.
method Gaussian mixture models (GMMs) and Genetic Algorithms (GAs) for optimal projection.
result The approach effectively detects informative structures in multivariate datasets.
Projection pursuit model improves Gaussian process regression for high-dimensional data.
problem Scalability issues with traditional Gaussian process models in high dimensions.
method Additive Gaussian process regression with dimension expansion and gradient descent.
result The proposed method approximates more complex functions and outperforms traditional models.
Experiment evaluates hospital case cost prediction models using Azure ML.
problem Accurate hospital case cost modelling for efficient financial management.
method Azure Machine Learning Studio tool for comparing 14 regression models.
result Robust regression, boosted decision tree, and decision forest models outperformed others.
This paper introduces generalized betas accounting for higher order co-moment effects.
problem Financial returns data often deviate from normal assumptions in terms of higher order moments and contain outliers.
method Introduces CAPI and PP framework to calculate generalized betas optimizing the CAPI objective.
result Generalized betas optimize the CAPI objective, accounting for higher order co-moment effects.
Optimal projections enhance Naive Bayes classification.
problem Improving Naive Bayes classification accuracy.
method Projection pursuit to find optimal linear projections.
result The approach substantially outperforms other models.
Paper analyzes and improves GPSP algorithm for block sparse signal recovery.
problem Recovering block sparse signals from noisy data.
method Group Projected Subspace Pursuit (GPSP) with convergence analysis and feature selection criteria.
result GPSP exactly recovers true block sparse signals under certain conditions.
This paper improves forest pruning to balance accuracy and interpretability.
problem Limited interpretability of regression forests.
method Lasso-pruning and theoretical analysis of regression forests.
result Pruned regression forests can achieve equal or better accuracy than unpruned ones, with significant size reduction.
The study examines the distribution of projections of Gaussian data points and its implications for learning models.
problem Understanding the distribution of projections of Gaussian data points in high dimensions.
method Analyzes the asymptotic behavior of projections of i.i.d. standard Gaussian vectors in Rd onto m-dimensional subspaces. result Establishes bounds on the Wasserstein radius of the set of probability distributions arising from these projections.
Projected random forests improve circular data prediction with adaptive arc length and finite-sample coverage.
problem Regression with circular responses.
method Adapting linear-response models to circular data using projection and random forest out-of-bag mechanism.
result Projected random forest out-of-bag conformal prediction sets are more efficient and shorter than alternative methods.
The study examines how bias affects hypothesis formation in neural networks.
problem Characterizing the impact of bias on hypothesis formation in neural networks.
method An automated data-driven projection pursuit neural network to extract and select features for binary classification.
result The refinement of a working hypothesis converges to a robust multivariate perception of data.
Decision forests, including Random Forests and Gradient Boosting Trees, have recently demonstrated state-of-the-art performance in a variety of machine learning settings. Decision forests are typically ensembles of axis-aligned decision trees; that is, trees that split only along feature dimensions. In contrast, many r…
New framework tests general high-dimensional hypotheses.
problem Testing general and complex hypotheses in high-dimensional models.
method Hypothesis adaptive projection pursuit framework.
result Asymptotically exact and powerful inference method for general functionals.
In this paper, we propose a new algorithm for exploratory projection pursuit. The basis of the algorithm is the insight that previous approaches used fairly narrow definitions of interestingness / non interestingness. We argue that allowing these definitions to depend on the problem / data at hand is a more natural app…
We study the problem of determining the optimal low dimensional projection for maximising the separability of a binary partition of an unlabelled dataset, as measured by spectral graph theory. This is achieved by finding projections which minimise the second eigenvalue of the graph Laplacian of the projected data, whic…
KOD detects outliers in high-dimensional data.
problem Challenges in outlier detection in high-dimensional settings.
method Kernel transformation followed by projection pursuit approach with ensemble of directions and result combination.
result Empirical evaluations show effectiveness on various datasets.
NGCA identifies non-Gaussian components in multidimensional data.
problem Identifying non-Gaussian components in multidimensional data.
method Uses relative entropy to approximate the non-Gaussian subspace.
result Algorithm approximates non-Gaussian subspace with polynomial time complexity.
Proposes rpf-kernel for clustering via random projection forests.
problem Clustering similar data points while distinguishing them from dissimilar ones.
method Random projection forests to learn a similarity kernel.
result rpf-kernel effectively clusters data with competitive performance.
In this paper, auto-associative models are proposed as candidates to the generalization of Principal Component Analysis. We show that these models are dedicated to the approximation of the dataset by a manifold. Here, the word "manifold" refers to the topology properties of the structure. The approximating manifold is …
Paper presents efficient computation of robust Wasserstein distance using Riemannian optimization.
problem Intractability of optimizing Projection Robust Wasserstein (PRW) distance due to non-convexity and non-smoothness.
method Riemannian optimization to efficiently compute PRW/Wasserstein Projection Pursuit (WPP) distance.
result The original formulation of PRW/WPP can be efficiently computed in practice, providing better behavior than its convex relaxation.
We propose a novel methodology, forest floor, to visualize and interpret random forest (RF) models. RF is a popular and useful tool for non-linear multi-variate classification and regression, which yields a good trade-off between robustness (low variance) and adaptiveness (low bias). Direct interpretation of a RF model…
A system uses randomisation to explore data guided by user knowledge and interests.
problem Creating an efficient exploratory data analysis system aware of user background knowledge and interests.
method Model user background knowledge with tiles, use constrained randomisation for efficient implementation, and apply linear projection pursuit to find informative views.
result The method is robust under noise, fast for interactive use, and gives understandable results for real-world data.
New pursuit algorithm for ML-CSC model with improved stability and dictionary learning.
problem Lack of exact pursuit algorithms and conditions for non-empty model in ML-CSC.
method Projection approach for pursuit algorithm, stability bounds, practical alternatives, online dictionary learning.
result Sound pursuit algorithm and practical dictionary learning for ML-CSC model.
A new method for generating time-dependent densities efficiently.
problem Computational difficulties in deep learning for temporal density modeling.
method Projection-based optimal transport and transport splines.
result The method is highly competitive with state-of-the-art normalizing flows.
Random Forests [Breiman:2001] (RF) are a fully non-parametric statistical method requiring no distributional assumptions on covariate relation to the response. RF are a robust, nonlinear technique that optimizes predictive accuracy by fitting an ensemble of trees to stabilize model estimates. The randomForestSRC packag…
This paper considers a recently emerged hyperspectral unmixing formulation based on sparse regression of a self-dictionary multiple measurement vector (SD-MMV) model, wherein the measured hyperspectral pixels are used as the dictionary. Operating under the pure pixel assumption, this SD-MMV formalism is special in that…
Exact Gaussian Process (GP) regression has O(N^3) runtime for data size N, making it intractable for large N. Many algorithms for improving GP scaling approximate the covariance with lower rank matrices. Other work has exploited structure inherent in particular covariance functions, including GPs with implied Markov st…
SLIC-UAV monitors forest recovery using UAVs and machine learning.
problem Challenges in monitoring forest recovery, especially in logged tropical forests.
method Novel pipeline for UAV imagery analysis, combining crown labelling, species classification, and superpixel segmentation.
result SLIC-UAV achieves high accuracy in species mapping, from 79.3% to 90.5%.
The paper provides bounds for high-dimensional U-statistics with novel order-explicit inequalities.
problem Bounding the deviation of high-dimensional U-statistics from their Hájek projections.
method Develops novel order-explicit moment inequalities for higher-order Hoeffding components.
result The maximum deviation of a high-dimensional U-statistic from its Hájek projection is of order Op(φbn−1log2(dn)). Thompson Sampling improves pursuit-evasion coordination.
problem Optimizing pursuer behavior to capture an evader efficiently.
method Variant of Thompson Sampling applied to pursuit-evasion problems.
result Thompson Sampling reduces time-to-capture significantly.
Unified analysis of matching pursuit and coordinate descent methods.
problem Optimization of linear spaces using first-order methods.
method Unified analysis of matching pursuit and coordinate descent, providing rates for smooth and strongly convex objectives.
result Unified analysis leading to tightest known rates for steepest coordinate descent and accelerated convergence for matching pursuit.
From a fresh data science perspective, this thesis discusses the prediction of coronary artery disease based on genetic variations at the DNA base pair level, called Single-Nucleotide Polymorphisms (SNPs), collected from the Ontario Heart Genomics Study (OHGS). First, the thesis explains two commonly used supervised le…
rpForests uses random projections to speed up kNN search.
problem Efficient kNN search in high-dimensional data.
method Random projection forests aggregating results from multiple random projection trees.
result rpForests achieves fast decay in missing rate and kNN distance discrepancy.
Isometry pursuit identifies orthonormal submatrices from wide matrices.
problem Identifying isometric embeddings from wide matrices.
method A convex algorithm combining normalization and multitask basis pursuit.
result The method identifies isometric embeddings from interpretable dictionaries.
Unified view on matching pursuit and Frank-Wolfe algorithms with improved convergence rates.
problem Improving convergence rates for matching pursuit and Frank-Wolfe algorithms.
method Unified optimization perspective leading to explicit convergence rates.
result Sublinear (1/t) convergence for general smooth objectives and linear convergence for strongly convex objectives. Develops exact and invariant study-based decompositions for network meta-analysis.
problem Lack of exact contribution decompositions in network meta-analysis.
method Contrast-space projection formulation of NMA, study-based definition of direct and indirect evidence.
result Exact covariance-aware decompositions of NMA estimator into direct and indirect contributions.
We study a form of cyclic pursuit on Riemannian manifolds with positive injectivity radius. We conjecture that on a compact manifold, the piecewise geodesic loop formed by connecting consecutive pursuit agents either collapses in finite time or converges to a closed geodesic. The main result is that this conjecture is …
A new algorithm improves SSC clustering accuracy with low complexity.
problem Sparse Subspace Clustering accuracy loss in time efficiency.
method Active Orthogonal Matching Pursuit (Active OMP-SSC) for improved clustering accuracy.
result Improves clustering accuracy of OMP-SSC with low computational complexity.
Study of pursuit-evasion game on sphere and its relation to planar Apollonius circle.
problem Analyzing pursuit-evasion game on a sphere and its properties.
method Extending classical planar pursuit-evasion game to spherical geometry, studying equilibrium intercept points and their relation to Apollonius domain.
result Condition for intercept point to belong to Apollonius domain on sphere, analogous to planar game.
New algorithms separate singing voices from accompaniment using complex and quaternionic principal component pursuit.
problem Separating singing voices from instrumental accompaniment using phase information.
method Extended principal component pursuit to complex and quaternionic cases, developed new proximity operators, applied inexact augmented Lagrange multiplier algorithm.
result Phase information improves singing voice separation.