This paper surveys various methods for dimensionality reduction and nearest neighbor search.
problem Efficiently reducing high-dimensional data to lower dimensions while preserving essential information.
method Linear and nonlinear random projections, including sparse random projections, random Fourier Features, and Random Kitchen Sinks.
result Various methods for dimensionality reduction and nearest neighbor search are explained and compared.
Proposes a method for modeling random objects in metric spaces using random effects.
problem Modeling random objects in non-Euclidean spaces with random effects.
method Nonlinear Fréchet-based algorithm for M-estimation.
result Consistent estimation of prediction target under random-effects formulation.
Paper analyzes and proves convergence of a new method for solving complex PDEs.
problem Solving high-dimensional nonlinear PDEs and PIDEs with random neural networks.
method Random deep splitting method using random neural networks.
result The method converges to the unique viscosity solution of nonlinear PDEs and PIDEs.
RFpredInterval package builds prediction intervals for random forests and boosted forests.
problem Quantifying uncertainty in random forest and boosted forest point predictions.
method 16 methods to build prediction intervals with random forests and boosted forests.
result The proposed method outperforms existing methods in building prediction intervals.
In this paper, we study randomized reduction methods, which reduce high-dimensional features into low-dimensional space by randomized methods (e.g., random projection, random hashing), for large-scale high-dimensional classification. Previous theoretical results on randomized reduction methods hinge on strong assumptio…
New method speeds up solving orthogonality constrained problems.
problem Solving orthogonality constrained problems efficiently.
method Riemannian optimization and Riemannian preconditioning.
result Preconditioning improves computational costs and convergence.
New methods improve prediction performance and reduce computation time in boosting and random forest models.
problem Improving prediction performance and reducing computation time in boosting and random forest models.
method Random tree depth injection approach for Boosting and Random Forests.
result The new methods can improve prediction performance and reduce computation time by up to 40%.
The paper analyzes the randomized midpoint method for Langevin diffusions, revealing biases and asymptotic properties.
problem Analyzing biases and asymptotic properties of the randomized midpoint method for Langevin diffusions.
method Characterization of stationary distribution and asymptotic normality for numerical integration.
result The step-size needs to go to zero for the method to be asymptotically unbiased.
The standard method of generating random weights and biases in feedforward neural networks with random hidden nodes, selects them both from the uniform distribution over the same fixed interval. In this work, we show the drawbacks of this approach and propose a new method of generating random parameters. This method en…
In this paper we present a convergence rate analysis of inexact variants of several randomized iterative methods. Among the methods studied are: stochastic gradient descent, stochastic Newton, stochastic proximal point and stochastic subspace ascent. A common feature of these methods is that in their update rule a cert…
Random feature approximation speeds up spectral methods and improves learning rates.
problem Improving the efficiency and generalization of spectral methods in large-scale algorithms.
method Combining random feature approximation with spectral regularization methods.
result Optimal learning rates for estimators over various regularity classes, including those not in the RKHS.
Although the methods of bagging and random forests are some of the most widely used prediction methods, relatively little is known about their algorithmic convergence. In particular, there are not many theoretical guarantees for deciding when an ensemble is "large enough" --- so that its accuracy is close to that of an…
We present Random Partition Kernels, a new class of kernels derived by demonstrating a natural connection between random partitions of objects and kernels between those objects. We show how the construction can be used to create kernels from methods that would not normally be viewed as random partitions, such as Random…
Label ranking aims to learn a mapping from instances to rankings over a finite number of predefined labels. Random forest is a powerful and one of the most successful general-purpose machine learning algorithms of modern times. In this paper, we present a powerful random forest label ranking method which uses random de…
Random feature method approximates operators with theoretical guarantees and reduced computation.
problem Approximating operators between infinite dimensional Banach spaces using machine learning.
method Random feature operator learning method with theoretical guarantees and error bounds.
result The random feature method can achieve similar or better test errors than kernel-based methods and neural networks with significantly reduced training times.
Corrects bias in random sampling matrices for improved ML methods.
problem Inversion bias in random sampling matrices hampers ML applications.
method Corrects inversion bias for various random sampling methods.
result Establishes local convergence rates for sub-sampled Newton methods.
Efficient search methods can outperform random search on challenging tasks.
problem Comparing the performance of efficient and random search methods in neural architecture search.
method Comparison of weight sharing and random search methods on progressively larger search spaces for image classification and detection.
result Efficient search methods can provide substantial gains over random search on large, realistic tasks.
Randomized control methods improve asset pricing and performance analysis.
problem Challenges in drawing inferences from traditional random portfolios in performance evaluation.
method Geometric random walks and Markov chain Monte Carlo methods to construct flexible control groups.
result Captured premia associated with size, value, quality, and momentum in a constrained setting.
Kernel method has been developed as one of the standard approaches for nonlinear learning, which however, does not scale to large data set due to its quadratic complexity in the number of samples. A number of kernel approximation methods have thus been proposed in the recent years, among which the random features metho…
Paper proposes a new method combining random forests and Lasso selection.
problem Improving random forest performance by applying Lasso regression.
method Adaptive Lasso weighting applied to random forest predictions.
result Unified framework strictly outperforms other methods in simulations and real-world datasets.
In (\cite{zhang2014nonlinear,zhang2014nonlinear2}), we have viewed machine learning as a coding and dimensionality reduction problem, and further proposed a simple unsupervised dimensionality reduction method, entitled deep distributed random samplings (DDRS). In this paper, we further extend it to supervised learning …
In this paper, we will show an unprecedented method to accelerate training and improve performance, which called random gradient (RG). This method can be easier to the training of any model without extra calculation cost, we use Image classification, Semantic segmentation, and GANs to confirm this method can improve sp…
Enhances random forest consistency and introduces DMRF for improved performance.
problem Improving the consistency and efficiency of random forest algorithms.
method Strengthened proof methods and propose DMRF algorithm.
result DMRF achieves better theoretical and experimental performance than previous variants.
We show that for any integers k and g, with g at least two, there are infinitely many closed hyperbolic 3-manifolds which are integral homology spheres with Casson invariant k, and Heegaard genus equal to g. This existence result is shown using random methods, using a model of random 3-manifolds arising from random wal…
This work estimates edge weights of edge-reinforced random walks using observed data.
problem Statistical estimation of edge weights in edge-reinforced random walks.
method Proposes an estimator based on the generalized method of moments using the magic formula and hyperbolic Gaussian structure.
result Analyzes the sample complexity of the proposed estimator.
Recently, the binary expansion testing framework was introduced to test the independence of two continuous random variables by utilizing symmetry statistics that are complete sufficient statistics for dependence. We develop a new test based on an ensemble approach that uses the sum of squared symmetry statistics and di…
A new method for efficient nonlinear process monitoring using random Bernoulli features.
problem High computational demands and real-time responsiveness in online monitoring systems.
method Random Bernoulli principal component analysis to capture nonlinear patterns efficiently.
result The proposed methods offer excellent scalability and reduced computational complexity.
New method stabilizes machine learning predictions across random seeds.
problem Machine learning predictions vary across random seeds, causing instability.
method Introduces adaptive cross-bagging to eliminate seed dependence.
result Adaptive cross-bagging achieves targeted stability in debiased machine learning.
A novel unsupervised outlier detection method using Randomized PCA Forest.
problem Unsupervised outlier detection in datasets.
method Randomized Principal Component Analysis (RPCA) Forest for deriving an outlier score.
result Superior performance compared to classical and state-of-the-art methods.
In this work, a method of random parameters generation for randomized learning of a single-hidden-layer feedforward neural network is proposed. The method firstly, randomly selects the slope angles of the hidden neurons activation functions from an interval adjusted to the target function, then randomly rotates the act…
Develops an empirical likelihood framework for random forests and ensembles.
problem Quantifying the statistical uncertainty of random forests and ensembles.
method Empirical likelihood framework exploiting the incomplete U-statistic structure of ensemble predictions. result Modified empirical likelihood statistic achieves accurate coverage and practical reliability.
HARFE approximates sparse additive functions using random features and ridge regression.
problem Approximating high-dimensional sparse additive functions.
method Hard-ridge random feature expansion with sparse ridge regression and hard-thresholding pursuit.
result HARFE method converges with a given error bound and achieves lower error than other algorithms.
Empirical study shows Randomized Signature Methods improve portfolio optimization in financial markets.
problem Drift estimation in non-linear, non-parametric financial markets is challenging.
method Applied Randomized Signature Methods for non-linear, non-parametric drift estimation in multi-variate financial markets.
result Randomized Signature Methods provide features on the same scale and improve portfolio optimization in real-world settings.
A new method improves graph random features with quasi-Monte Carlo techniques.
problem Improving the accuracy of graph random features.
method Induces negative correlations in random walks using antithetic termination.
result Strong theoretical guarantees on lower-variance estimators of the Laplacian kernel.
A new method for LDA using randomized Kaczmarz improves accuracy for large datasets.
problem Efficiently performing LDA on large datasets.
method Randomized Kaczmarz method applied to linear discriminant analysis.
result The method achieves comparable accuracy to full data LDA.
Develops a method for random manifolds and submanifolds, focusing on 3-ball knots.
problem Understanding random submanifolds in triangulated manifolds.
method Coloring vertices of triangulated manifolds to generate random submanifolds.
result Probability of generating an unknot decays exponentially in 3-ball with 3 colors.
Unified methodology for statistical inference in least squares and PCA via randomized sketching.
problem Statistical inference in least squares and PCA problems.
method Randomized sketching and projections, asymptotic normality of quadratic forms.
result Unified statistical inference methods for various sketching distributions.
Orthogonal random features approximate a Bessel kernel, offering sharper bounds than random Fourier features.
problem Approximating Gaussian kernel efficiently for large datasets.
method Use of Haar orthogonal matrices to construct orthogonal random features and analyze their bias and variance.
result Orthogonal random features approximate a Bessel kernel, not the Gaussian kernel, with sharper bounds.
The random subspace method, known as the pillar of random forests, is good at making precise and robust predictions. However, there is not a straightforward way yet to combine it with deep learning. In this paper, we therefore propose Neural Random Subspace (NRS), a novel deep learning based random subspace method. In …
Improved kernel ridge regression for large datasets using weighted random binning.
problem Efficiently approximating kernel matrices for large-scale datasets.
method Introduced weighted random binning features for locality sensitive hashing.
result Weighted random binning features generate Gaussian processes of any desired smoothness.
We improve random forest consistency and performance with DMRF, a new variant.
problem Improving the consistency and performance of random forest models.
method Developed DMRF, a data-driven multinomial random forest, by modifying proof methods and improving data utilization.
result DMRF achieves strong consistency with probability 1, surpassing previous models in classification tasks.
New method reduces variance in random coordinate descent for Langevin Monte Carlo.
problem Efficient sampling from log-concave distributions in high dimensions.
method Introduces RCAD, a variance reduction technique for RCD-LMC.
result RCAD-O-LMC and RCAD-U-LMC converge within the same number of iterations as classical LMC methods, saving computational cost.
Extends random feature analysis to spectral methods and improves learning rates.
problem Improving generalization properties of spectral methods in large-scale learning.
method Extends random feature analysis to a broad class of spectral regularization techniques, including gradient descent and Nesterov method.
result Obtains optimal learning rates for regularity classes, including those not in the RKHS.
Enhances supervised visualization for unseen data using autoencoders and random forest.
problem Lack of generalization to unseen test sets in supervised dimensionality reduction.
method Combines autoencoder and random forest proximities for out-of-sample extension.
result 40% reduction in training time with 10% of training data, achieving consistent quality.
Subsampled Randomized Hadamard Transform (SRHT), a popular random projection method that can efficiently project a d-dimensional data into r-dimensional space (r≪d) in O(dlog(d)) time, has been widely used to address the challenge of high-dimensionality in machine learning. SRHT works by rotating the input …
Random shuffle method boosts HF dataset size 10-21 times.
problem Narrow dataset cardinality in HF clinical studies.
method Random shuffle method to enhance dataset size.
result Enhanced HF dataset size 10-21 times.
New local-search methods close the gap in sparse tensor PCA.
problem Sparse tensor PCA underperforms compared to other methods.
method Proposes new local-search methods including greedy and random-threshold variants.
result Proves local-search methods close the gap to best known polynomial-time procedures.
Loopy belief propagation (LBP), which is equivalent to the Bethe approximation in statistical mechanics, is a message-passing-type inference method that is widely used to analyze systems based on Markov random fields (MRFs). In this paper, we propose a message-passing-type method to analytically evaluate the quenched a…