This paper enhances privacy-preserving randomized power method for large datasets.
problem Privacy issues in applying randomized power method to large datasets containing personal information.
method Proposes enhanced privacy-preserving variants of the randomized power method, including a variant with reduced noise and a decentralized framework.
result Tighter convergence bounds and empirical comparisons with previous work in real recommendation datasets.
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…
ParPIC clusters directed graphs using random walks and diffusion operators.
problem Challenges in vertex-level clustering for directed graphs due to edge directionality.
method Parametrized Power-Iteration Clustering (ParPIC) based on reversible random walks and diffusion operators.
result ParPIC achieves competitive clustering accuracy with improved scalability compared to spectral and teleportation-based methods.
Paper refutes conjecture on tensor power iteration convergence in overcomplete models.
problem Understanding convergence of tensor power iteration in overcomplete random tensors.
method Analysis of tensor power iteration dynamics from random initialization.
result Polynomially many steps are necessary for convergence, refutes logarithmic conjecture.
A new method improves convergence in low-rank approximation.
problem Efficiently solving large-scale numerical linear algebra problems.
method Error-Powered Sketched Inverse Iteration (EPSI) Method.
result Convergence rate improves at least linearly with sketch size.
Random forests are a type of ensemble method which makes predictions by combining the results of several independent trees. However, the theory of random forests has long been outpaced by their application. In this paper, we propose a novel random forests algorithm based on cooperative game theory. Banzhaf power index …
New method achieves faster calibration without randomization.
problem Calibrating probabilistic forecasts in adversarial settings.
method Using interval forecasts and the power of two choices.
result Achieves O(1/T) calibration error rate without randomization. Graph neural networks (GNNs) are powerful machine learning models for various graph learning tasks. Recently, the limitations of the expressive power of various GNN models have been revealed. For example, GNNs cannot distinguish some non-isomorphic graphs and they cannot learn efficient graph algorithms. In this paper,…
Power laws detected in financial data, modeled with random multipliers.
problem Detecting power laws in financial data.
method Investigated data from financial instruments, proposed a model based on sums of Maxwell-Boltzmann distributions with random multipliers.
result Detected power laws with various exponents in financial data, proposed a universal model.
Improved MMD test for two-sample testing with random Fourier features.
problem Quadratic-time complexity of MMD test for large-scale analysis.
method Approximated MMD test using random Fourier features, investigating time-power trade-off.
result Sub-quadratic time complexity with same minimax separation rates as MMD test.
New random feature maps for Laplacian and related kernels.
problem Challenges in approximating the Laplacian kernel and its generalizations.
method Developed random feature maps for Laplacian and related kernels, providing efficient sampling schemes.
result Demonstrated the efficacy of these random feature maps on real datasets.
Low-rank structure have been profoundly studied in data mining and machine learning. In this paper, we show a dense matrix X's low-rank approximation can be rapidly built from its left and right random projections Y1=XA1 and Y2=XTA2, or bilateral random projection (BRP). We then show power scheme can further…
Surveying random sections on Kähler manifolds, leading to metrics.
problem Understanding statistics of random sections on Kähler manifolds.
method Analyzing tensor powers of line bundles.
result Induced metrics from random sections.
New method improves feature importance assessment in random forests.
problem Improving feature importance measures for random forests.
method Hypothesis testing via self-normalized feature-residual correlation test (FACT).
result The method provides theoretically justified feature importance tests with controlled type I error and appealing power.
We present a model for random simple graphs with a degree distribution that obeys a power law (i.e., is heavy-tailed). To attain this behavior, the edge probabilities in the graph are constructed from Bertoin-Fujita-Roynette-Yor (BFRY) random variables, which have been recently utilized in Bayesian statistics for the c…
G-computation improves clinical trial power with machine learning.
problem Balancing prognostic factors in randomized trials to prevent near-confounders.
method G-computation with penalized models (Lasso, Elasticnet) and algorithm-based methods (neural network, SVM, super learner).
result G-computation with Elasticnet and splines reduces variance and increases power in RCTs.
New method explains GNNs using power iteration clustering.
problem Mysterious mechanism of message passing in GNNs.
method Subspace power iteration clustering (SPIC) models.
result Message passing in GNNs can be understood through power iteration.
We accelerate the power method for strong low-rank approximation using fast sketching.
problem Efficiency bottleneck in power method for large target ranks.
method Developed an algorithmic and theoretical framework for accelerating the power method using fast sketching.
result Simple and provably efficient methods for singular value decomposition, low-rank factorization, and Nyström approximation.
New method detects biomarker-treatment interactions in clinical trials.
problem Detecting interactions between high-dimensional biomarkers and treatments in randomized trials.
method Two-stage penalized regression screening using ridge regression for multivariate screening.
result Ridge regression screening provides greater power than traditional methods in correlated data.
GNNs with random node initialization are shown to be universally expressive.
problem Limitations of standard GNNs in distinguishing graphs.
method Random node initialization (RNI) to enhance GNNs' expressive power.
result GNNs with RNI are proven to be universally expressive.
Power-law spectrum of random feature model is preserved in neural networks.
problem Preserving power-law spectrum in neural networks through random feature model.
method Characterized eigenvalues of population random-feature covariance using dyadic head-tail decomposition and Wick chaos expansions.
result Power-law exponent α is inherited from input covariance, modified by a logarithmic correction. 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…
Boosts change-point detection power with optimal sub-sampling.
problem Power loss in sequential change-point detection from large history data.
method Optimal sub-sampling of history data before kernel-based detection procedures.
result Improved detection performance in extensive experiments.
Bandlimited random neural networks may not approximate all functions perfectly.
problem Expressive power of shallow neural networks with bandlimited random weights.
method Ridgelet analysis for deriving approximation error lower bounds.
result Bandlimited random weights can lead to non-zero approximation error.
Study reveals neural scaling laws in random graphs and natural language models.
problem Understanding the origin of neural scaling laws in complex systems.
method Examined scaling laws in transformers trained on random walks and simplified natural language models.
result Neural scaling laws emerge in the absence of power law structure in data correlations.
Paper improves power of conditional randomization tests.
problem Improving power of conditional randomization tests.
method Introducing a new cost function to maximize test statistic power.
result Consistently increases the number of correct discoveries.
The paper analyzes the variance of different shuffling methods in stochastic gradient descent.
problem Understanding the variance of different shuffling methods in stochastic gradient descent.
method Power spectral density analysis to study the noise sequences of stochastic gradients.
result The stationary variances of iterates decrease in the order of SGD, SGD-RR, and SGD-SO.
LightOn OPUs accelerate randomized numerical linear algebra, reducing computational costs.
problem Computational bottleneck in randomization step for large-scale linear algebra.
method Near constant-time linear random projections from LightOn OPUs.
result Significant acceleration of RandNLA algorithms with negligible precision loss.
Graph Neural Networks struggle on random graphs without node identifiers.
problem Graph Neural Networks' limitations on random graphs without node identifiers.
method Study of Graph Neural Networks and Structural Graph Neural Networks convergence on large random graphs.
result Structural Graph Neural Networks are more powerful and universal than Graph Neural Networks on random graphs.
Power of network tests degrades when vertices are misaligned.
problem Power loss in network hypothesis testing due to vertex shuffling.
method Theoretical analysis and simulations of Frobenius norm differences in random dot product and stochastic block models.
result Shuffling vertices can significantly reduce the power of network tests.
Effects of randomness on non-integer power law tails in multiplicatively interacting stochastic processes are investigated theoretically. Generally, randomness causes decrease of the exponent of tails and the growth rate of processes. Explicit calculations are performed for two examples: uniformly distributed and two p…
Fold maps associated to geodesic random walks on curved spaces.
problem Understanding the behavior of geodesic random walks on curved surfaces.
method Analyzing mappings from the unit tangent sphere to a manifold with non-positive curvature.
result For odd powers of the unit tangent sphere, these mappings are fold maps.
fcHMRF-LIS controls FDR in neuroimaging data, improving power and scalability.
problem Complex spatial dependencies and high variability in FDR control methods for neuroimaging data.
method fcHMRF-LIS integrates LIS-based testing with fcHMRF to model spatial structures efficiently.
result fcHMRF-LIS achieves accurate FDR control, lower FNR, and higher true positives compared to existing methods.
Critical volatility triggers log-normal to power-law transitions in interconnected systems.
problem Understanding the transition from log-normal to power-law distributions in interconnected systems.
method Analyzing an infinite option-on-option chain model, deriving a critical volatility threshold.
result A critical volatility threshold of approximately 250.66% for unconditional cases, dropping to 125.3% with selective survival.
Random Hyperboxes is a simple yet effective ensemble classifier.
problem Improving classification accuracy using ensemble methods.
method Random subsets of sample and feature spaces are used to train individual hyperbox-based classifiers, which are then combined into an ensemble.
result The proposed classifier outperforms other fuzzy min-max neural networks and ensemble methods on 20 datasets.
Tensor CANDECOMP/PARAFAC (CP) decomposition has wide applications in statistical learning of latent variable models and in data mining. In this paper, we propose fast and randomized tensor CP decomposition algorithms based on sketching. We build on the idea of count sketches, but introduce many novel ideas which are un…
Bayesian nonparametric approaches, in particular the Pitman-Yor process and the associated two-parameter Chinese Restaurant process, have been successfully used in applications where the data exhibit a power-law behavior. Examples include natural language processing, natural images or networks. There is also growing em…
Detects dense subhypergraphs in heterogeneous random hypergraphs.
problem Testing for the existence of a dense subhypergraph in heterogeneous random hypergraphs.
method Established detection boundaries and constructed asymptotically powerful and adaptive tests.
result Developed tests for distinguishing between null and alternative hypotheses.
Develops deep learning methods for solving S-shaped utility maximisation problems.
problem Optimizing portfolios with S-shaped utility and random benchmarks.
method Uses deep learning and duality methods to solve the Hamilton-Jacobi-Bellman equation and adjoint equation.
result Demonstrates the accuracy of deep learning methods for non-concave utility maximisation problems.
Gradient boosting with randomized trees reduces discontinuities and complexity.
problem Discontinuities in regression functions due to sparse training data.
method Gradient boosting machine with partially randomized decision trees.
result Improves robustness and computational efficiency of gradient boosting.
Exact selective inference with randomization for Gaussian regression models.
problem Exact selective inference in Gaussian regression models.
method Introduces a pivot for exact selective inference with randomization, reducing the problem to a bivariate truncated Gaussian distribution.
result Our pivot leads to exact inference and produces narrower confidence intervals than related methods.
Study reveals a universal formula for knotting in random equilateral polygons.
problem Probability of knotting in equilateral random polygons.
method Extensive Monte Carlo simulations with improved algorithms and knot invariants.
result A universal scaling formula for knotting probability with number of edges, involving exponential and power law factors.
A wide variety of deep learning techniques from style transfer to multitask learning rely on training affine transformations of features. Most prominent among these is the popular feature normalization technique BatchNorm, which normalizes activations and then subsequently applies a learned affine transform. In this pa…
While statistical learning methods have proved powerful tools for predictive modeling, the black-box nature of the models they produce can severely limit their interpretability and the ability to conduct formal inference. However, the natural structure of ensemble learners like bagged trees and random forests has been …
Kernel methods are powerful and flexible approach to solve many problems in machine learning. Due to the pairwise evaluations in kernel methods, the complexity of kernel computation grows as the data size increases; thus the applicability of kernel methods is limited for large scale datasets. Random Fourier Features (R…
QR-learner estimates individual treatment effects using external data.
problem Limited power to detect individual treatment effects in randomized trials.
method Model-agnostic learner that estimates conditional average treatment effects (CATE) using external data.
result QR-learner reduces mean squared error and can recover true CATE.
Randomized hierarchical clustering tests for stability and detects clusters.
problem Greedy hierarchical clustering's sensitivity to data perturbations.
method Randomization scheme and p-values at each node.
result Valid hypothesis testing procedures for clustering results.
A hierarchical model shows how scaling laws emerge from sequential feature recovery.
problem Emergence of scaling laws from feature learning in multi-layer networks.
method Layer-wise spectral algorithm adapted to compositional structure, sequential feature detection.
result Sequential detection of latent features, leading to explicit power-law decay of prediction error.