New stochastic gradient descent with random search directions improves efficiency and convergence.
problem Efficiency and convergence of stochastic gradient descent methods.
method Developed a new class of stochastic gradient descent algorithms with random search directions.
result Established almost sure convergence and provided Lp rates of convergence. New algorithms estimate Hessians using random directions for faster stochastic optimization.
problem Efficiently estimating Hessians for stochastic optimization.
method Generalized Hessian estimators using random directions and noisy function measurements.
result Asymptotically unbiased estimators with lower bias for more measurements.
Randomized spectral co-clustering speeds up large-scale directed networks.
problem Co-clustering directed networks efficiently for large-scale data.
method Randomized spectral co-clustering algorithms using random-projection and random-sampling techniques.
result Theoretical and numerical validation of approximation and misclustering error rates.
This work improves structured prediction by learning the balance between signal and random noise.
problem Structured prediction with random perturbations.
method Learning the variance of randomized structured predictors to balance signal and noise.
result Learning the balance improves structured prediction effectiveness.
NetOTC compares and aligns directed or undirected networks via random walk transitions.
problem Comparing and aligning networks of different types and sizes.
method NetOTC uses a transport-based approach to find optimal transition couplings of random walks.
result NetOTC quantifies network differences and provides vertex and edge alignments.
We introduce a novel harmonic analysis for functions defined on the vertices of a strongly connected directed graph of which the random walk operator is the cornerstone. As a first step, we consider the set of eigenvectors of the random walk operator as a non-orthogonal Fourier-type basis for functions over directed gr…
RVFL NNs perform well without direct links and output bias for regression.
problem Effect of direct links and output bias on RVFL performance.
method Classical and two new methods for generating hidden nodes' parameters tested.
result Direct links and output bias do not significantly improve RVFL accuracy for typical nonlinear regression problems.
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.
Study relaxes identification assumptions for natural direct effects in non-randomized settings.
problem Identifying causal direct effects under unmeasured confounding.
method Developed relaxed conditions for identifying natural direct effects in non-randomized settings.
result Identified natural direct effect under unmeasured confounding conditions.
Estimates mean of random vector with near-optimal error in all directions.
problem Estimating the mean of a random vector with direction-dependent accuracy.
method Proves existence of an estimator with near-optimal error in all directions under certain conditions.
result The estimator satisfies the error bound for all directions, with probability 1-δ.
Improved ridge regression with Frequent Directions for large-scale tasks.
problem Improving performance of ridge regression for large-scale data.
method Combines Frequent Directions with iterative optimization schemes.
result Achieves high accuracy in estimating bias and variance for sketched ridge regression.
We find the explicit expression for the equilibrium wealth distribution of the Directed Random Market process, recently introduced by Martínez-Martínez and López-Ruiz, which turns out to be a Gamma distribution with shape parameter 21. We also prove the convergence of the discrete-time process describing the…
New method clusters directed and undirected graphs without losing directional information.
problem Clustering directed graphs due to asymmetry in edge connectivity.
method Generalized Dirichlet Energy (GDE) and generalized spectral clustering (GSC).
result GSC outperforms existing methods in clustering accuracy and robustness.
The paper shows that relaxing assumptions about causal graphs can lead to exponentially large equivalence classes.
problem The size of Markov equivalence classes under relaxed assumptions.
method Analytical proofs for three settings: sparse random directed acyclic graphs, uniformly random acyclic directed mixed graphs, and uniformly random directed cyclic graphs.
result Exponentially large lower bounds for the expected size of Markov equivalence classes.
Self-directed learners can minimize mistakes in online classification.
problem Minimizing mistakes in online classification with adaptive prediction order.
method Designing efficient self-directed learners for linear classification.
result Strong separation between worst-order and random-order learning for linear classification.
Direct optimization is an appealing framework that replaces integration with optimization of a random objective for approximating gradients in models with discrete random variables. A⋆ sampling is a framework for optimizing such random objectives over large spaces. We show how to combine these techniques to yiel…
Paper develops online statistical inference methods for stochastic optimization using Kiefer-Wolfowitz algorithms.
problem Online statistical inference of model parameters in stochastic optimization problems.
method Kiefer-Wolfowitz algorithm with random search directions, asymptotic distribution analysis.
result Developed valid confidence intervals for online statistical inference.
Study geodesic trees and exceptional directions in FPP on hyperbolic groups.
problem Understanding the geometry and uniqueness of geodesics in FPP on hyperbolic groups.
method Analyzing random geodesic trees and exceptional directions in the context of FPP on hyperbolic groups.
result The set of exceptional directions has strictly smaller Hausdorff dimension than the boundary, and hence has measure zero.
New method identifies valid IVs for bi-directional MR with invalid instruments.
problem Estimating causal effects from observational data with invalid instruments and unmeasured confounding.
method Theoretical investigation and cluster fusion-like method to discover valid IV sets.
result Theoretical demonstration and experimental validation of the method's effectiveness.
"Mixed Data" comprising a large number of heterogeneous variables (e.g. count, binary, continuous, skewed continuous, among other data types) are prevalent in varied areas such as genomics and proteomics, imaging genetics, national security, social networking, and Internet advertising. There have been limited efforts a…
New random forest variants achieve optimal performance in high dimensions.
problem Handling dependencies between features in high-dimensional data.
method Using oblique splits in random forests with general split directions.
result Achieved minimax optimal convergence rates in arbitrary dimension.
BayesMR estimates causal effects and directionality from genetic data.
problem Challenges in finding good genetic instruments and estimating causal effects.
method Bayesian Mendelian randomization approach that accounts for pleiotropy and reverse causation.
result BayesMR provides a posterior distribution over causal effects and uncertainty.
The study uses LSTM and random forests to forecast stock price movements for intraday trading.
problem Forecasting directional movements of stock prices for intraday trading.
method Employed random forests and LSTM networks to analyze S&P 500 constituent stocks.
result Multi-feature setting provided higher daily returns (0.64% using LSTM, 0.54% using random forests) compared to single-feature setting.
A new slicing method speeds up sliced Wasserstein estimation.
problem Efficiently estimating sliced Wasserstein distance.
method Random-Path Projecting Direction (RPD) for fast sampling.
result RPSW and IWRPSW show favorable performance in training generative models.
Study large deviations in random walks on Lie groups.
problem Large deviations in sub-Riemannian random walks.
method Prove large deviation principle for random walks on stratified Lie groups.
result Proved a large deviation principle with a rate function adapted to sub-Riemannian geometry.
New damping technique improves deep learning models by reducing noise in flat directions.
problem Improving generalization in deep learning models by reducing estimation noise in flat directions.
method Developed a novel random matrix theory based damping learner to reduce the shrinkage coefficient and improve generalization.
result Significant generalization improvements in logistic regression and deep neural networks experiments.
LayerNorm transformers have dead directions that can be read from their parameters alone.
problem Locating dead directions in LayerNorm transformers
method Using the inverse-scale direction of LayerNorm affine parameters
result Predicted dead direction matches measured bottom singular direction
New Teichmüller geodesic rays found with unique foliations.
problem Capturing generic directions in Teichmüller space.
method Using Chaika-Masur-Wolf and Durham-Zalloum work.
result First sublinearly-Morse geodesic rays with minimal non-uniquely ergodic foliations.
Paper proves causal direction can be inferred from data with limited randomness.
problem Inferring causal direction from observational data with limited randomness.
method Entropy measurement and structural causal models.
result Causal direction is identifiable for most causal models with limited entropy.
This paper compares imputation and direct parameter estimation methods for missing data in correlation matrix visualization.
problem Missing data challenges in estimating correlation coefficients for accurate visualization.
method Comparison of imputation and direct parameter estimation methods for handling missing data.
result Direct parameter estimation (DPER) outperforms imputation for accurate correlation matrix visualization.
Understanding the underlying mechanisms that enable the empirical successes of deep neural networks is essential for further improving their performance and explaining such networks. Towards this goal, a specific question is how to explain the "surprising" behavior of the same over-parametrized deep neural networks tha…
Study examines how body segments respond to random vibrations.
problem Understanding human body responses to random vibrations.
method 35 participants were tested with random noise signals. Multiple linear regression models were created to determine influential predictors of peak translational gains.
result Multiple predictors, including motion direction and body segment, significantly influence peak translational gains.
Online CPD for weighted and directed graphs using RDPG model.
problem Monitoring and detecting changes in weighted and directed graph data.
method Spectral embeddings of RDPG models for online updates and error-rate control.
result A lightweight online CPD algorithm with improved detection resolution and delay.
There is a large literature explaining why AdaBoost is a successful classifier. The literature on AdaBoost focuses on classifier margins and boosting's interpretation as the optimization of an exponential likelihood function. These existing explanations, however, have been pointed out to be incomplete. A random forest …
This paper refines bounds on random walk speed in Teichmüller space.
problem Understanding the speed of random walks on Teichmüller space.
method Analyzing Jenkins-Strebel directions and Lebesgue geodesics.
result The drift of random walks grows exponentially for typical geodesics and oscillates between linear and exponential for some geodesics.
Boltzmann-Gibbs distribution arises as the statistical equilibrium probability distribution of money among the agents of a closed economic system where random and undirected exchanges are allowed. When considering a model with uniform savings in the exchanges, the final distribution is close to the gamma family. In thi…
Sparse RSP routing improves graph exploration and classification.
problem Optimal randomized routing and distance measures on weighted graphs.
method Tsallis divergence regularization for sparse RSP.
result Sparse random walk converges to least-cost graph as temperature decreases.
Goal-directed Reinforcement Learning (RL) traditionally considers an agent interacting with an environment, prescribing a real-valued reward to an agent proportional to the completion of some goal. Goal-directed RL has seen large gains in sample efficiency, due to the ease of reusing or generating new experience by pro…
We propose a new Directed Continuous-Time Random Walk (CTRW) model with memory. As CTRW trajectory consists of spatial jumps preceded by waiting times, in Directed CTRW, we consider the case with only positive spatial jumps. Moreover, we consider the memory in the model as each spatial jump depends on the previous one.…
Study asset price bubbles using random matching and stochastic factors.
problem Understanding and modeling asset price bubbles through investor contagion.
method Developed a stochastic model of liquidity-based asset price bubbles using random matching mechanism.
result Derived conditions for arbitrage-free financial market models.
Study benchmarks classical models over quantum in DeFi yield prediction.
problem Accurate yield and performance forecasting for DeFi liquidity allocation.
method Benchmarked six models on Curve Finance pools' historical data.
result Classical models, especially XGBoost, outperform quantum models.
Study compares ML algorithms for predicting stock market directional bias.
problem Predicting the direction of stock market movements.
method Examined and contrasted logistic regression, decision tree, random forest, and a deep neural network.
result All models consistently reach above 50% in directional bias forecasting.
Reviews six finance topics, including 'radical complexity'.
problem None explicitly stated, focuses on research directions.
method Informal review and discussion of open questions.
result No specific key result mentioned, focuses on research directions.
In this paper we consider the problem of graph-based transductive classification, and we are particularly interested in the directed graph scenario which is a natural form for many real world applications. Different from existing research efforts that either only deal with undirected graphs or circumvent directionality…
The local geometry of high dimensional neural network loss landscapes can both challenge our cherished theoretical intuitions as well as dramatically impact the practical success of neural network training. Indeed recent works have observed 4 striking local properties of neural loss landscapes on classification tasks: …
Customer scoring models are the core of scalable direct marketing. Uplift models provide an estimate of the incremental benefit from a treatment that is used for operational decision-making. Training and monitoring of uplift models require experimental data. However, the collection of data under randomized treatment as…
A new method for approximating softmax and Gaussian kernels with reduced error.
problem Approximating softmax and Gaussian kernels with low error.
method Simplex Random Features (SimRFs) and SimRFs+.
result SimRFs provide the smallest MSE among weight-independent geometrically-coupled PRF mechanisms.
Several known results, by Rivin, Calegari-Maher and Sisto, show that an element φn∈Out(Fr), obtained after n steps of a simple random walk on Out(Fr), is fully irreducible with probability tending to 1 as n→∞. In this paper we construct a natural "train-track directed" random walk W on $…