The paper develops a method to sparsify magnetic Laplacians using multi-type spanning forests.
problem Sparsifying magnetic Laplacians for large and dense graphs.
method Sampling multi-type spanning forests using a determinantal point process.
result The method provides statistical guarantees for estimating the connection Laplacian.
Proves bounds on spanning two-forests and random cut sizes.
problem Counting spanning two-forests and estimating random cut sizes.
method Uses pairwise effective resistances and potential theory.
result Establishes bounds on the number of spanning two-forests and average cut size.
Differentiable clustering method using perturbed spanning forests.
problem Efficient clustering in trainable pipelines with noisy data.
method Stochastic perturbations of minimum-weight spanning forests.
result Method performs well even in challenging settings.
Study asymptotic expansion of graph Laplacian on discretized surfaces, relating spanning trees and cycle-rooted forests.
problem Asymptotic expansion of graph Laplacian on discretized surfaces.
method Relate spanning trees and cycle-rooted spanning forests to zeta-regularized determinants.
result Explicit formula for limit of cycle-rooted spanning forest probability and topological observables.
M4L-JMF tackles multi-typed objects learning, improving on M3L.
problem Learning from multi-typed objects with diverse features and labels.
method Joint matrix factorization to encode and factorize multi-typed bags and their instances.
result M4L-JMF outperforms existing methods on benchmark datasets.
We establish an asymptotic relation between the spectrum of the discrete Laplacian associated to discretizations of a half-translation surface with a flat unitary vector bundle and the spectrum of the Friedrichs extension of the Laplacian with von Neumann boundary conditions. As an interesting byproduct of our study, w…
Investigates stochastic networks on disordered lattices, converging to Brownian web in 2D.
problem Stochastic networks on disordered lattices.
method Directed spanning forests on randomly perturbed lattices.
result DSF converges to Brownian web in 2D under diffusive scaling.
Advances neural tri-factorization for clustering and discordance analysis of multi-typed data.
problem Challenges in analyzing heterogeneous, multimodal relational data.
method Deep collective matrix tri-factorization for spectral clustering and cluster association learning.
result Demonstrates efficacy over previous non-neural approaches in clustering and discordance analysis.
A result about spanning forests for graphs yields a short proof of Krebes's theorem concerning embedded tangles in links.
We study graph estimation and density estimation in high dimensions, using a family of density estimators based on forest structured undirected graphical models. For density estimation, we do not assume the true distribution corresponds to a forest; rather, we form kernel density estimates of the bivariate and univaria…
Let X and Y be infinite graphs, such that the automorphism group of X is nonamenable, and the automorphism group of Y has an infinite orbit. We prove that there is no automorphism-invariant measure on the set of spanning trees in the direct product X times Y. This implies that the minimal spanning forest corresponding …
SHAKE-GNN scales GNNs for large graphs with multi-scale representations.
problem Scaling Graph Neural Networks (GNNs) to large graphs.
method SHAKE-GNN uses a hierarchy of Kirchhoff Forests for stochastic multi-resolution graph decompositions.
result SHAKE-GNN achieves competitive performance on large-scale graph classification benchmarks.
CAUSE learns Granger causality from event sequences, outperforming existing methods.
problem Learning Granger causality from complex, interdependent event sequences.
method CAUSE uses a neural point process to capture interdependency and an attribution method to extract Granger causality.
result CAUSE outperforms state-of-the-art methods in inferring inter-type Granger causality.
We present a framework for incorporating prior information into nonparametric estimation of graphical models. To avoid distributional assumptions, we restrict the graph to be a forest and build on the work of forest density estimation (FDE). We reformulate the FDE approach from a Bayesian perspective, and introduce pri…
Paper offers a simple CDS approximation formula with high accuracy.
problem Lack of CDS levels for market appreciation of companies' default risk.
method Developed a global and transparent Equity-to-Credit (E2C) formula using random forest regression.
result Random forest regression with E2C formula achieves 87.3% out-of-sample accuracy in CDS approximations.
Framework for joint inference of network topology and interaction types in heterogeneous systems.
problem Joint inference of network topology, multi-type interaction kernels, and latent type assignments in heterogeneous interacting particle systems.
method Three-stage approach: shared structure recovery, discrete interaction type identification, and matrix factorization.
result The method yields accurate reconstruction of underlying dynamics and is robust to noise.
Predicts stock volatility using Twitter data and random forests.
problem Predicting stock implied volatility using Twitter data.
method Random forests with ablation study on different predictors, including Twitter attention and sentiment features.
result Certain sectors like Consumer Discretionary, Technology, Real Estate, and Utilities are easier to predict.
We propose a topological learning algorithm for the estimation of the conditional dependency structure of large sets of random variables from sparse and noisy data. The algorithm, named Maximally Filtered Clique Forest (MFCF), produces a clique forest and an associated Markov Random Field (MRF) by generalising Prim's m…
DOFEN improves DNN performance on tabular data benchmarks.
problem DOFEN tackles the performance gap between DNNs and tree-based models on tabular data.
method DOFEN uses a two-level rODT forest ensembling process inspired by oblivious decision trees.
result DOFEN achieves state-of-the-art results on the Tabular Benchmark.
The paper develops a neural network model for SPX option pricing.
problem Developing an empirical model for SPX option pricing.
method Formulated and rigorously evaluated several statistical models including neural network, random forest, and linear regression.
result The neural network model outperforms other models and Black-Scholes-Merton model for SPX option pricing.
Classification outperforms regression in portfolio construction, yielding higher Sharpe ratios.
problem Determining which machine learning approach (classification vs. regression) is more effective for portfolio construction.
method Used stacking ensemble of gradient boosted tree, random forest, and neural network models.
result Classification yields higher Sharpe ratios and economically significant alphas compared to regression.
Paper studies gradient fields from discrete Morse functions for watershed-cut computation.
problem Computing watershed-cuts from discrete Morse functions.
method Discrete Morse Theory and simplicial stacks.
result Minimum Spanning Forest of dual graph is induced by gradient vector field.
Paper introduces MVS to detect non-Markovian observations in reinforcement learning.
problem Real-world sensors violate Markov property, leading to suboptimal reinforcement learning performance.
method Uses prediction-based Markov Violation Score (MVS) combining random forest and ridge regression.
result MVS detects non-Markovian structure in observation trajectories, quantifying its impact.
Develops a new model for pricing without arbitrage opportunities.
problem Arbitrage opportunities in standard jump-diffusion models.
method Introduces a multi-type jump-diffusion model with diffusion-dependent jumps.
result Derives no-arbitrage condition linking drift to model parameters.
Research uses deep learning and copulas to predict multivariate survival data.
problem Handling right-censored and correlated multivariate survival data.
method Integrates deep learning, copula functions, and survival analysis. Uses copula-based activation functions to model nonlinear dependencies.
result Enhanced prediction accuracy for multivariate survival responses.
iMondrian forest combines isolation forest and Mondrian forest for better anomaly detection.
problem Anomaly detection in batch and online settings.
method Hybrid of isolation forest and Mondrian forest, using depth in Mondrian forest structure.
result iMondrian forest outperforms existing methods in batch and online settings.
Ensembles of randomized decision trees, usually referred to as random forests, are widely used for classification and regression tasks in machine learning and statistics. Random forests achieve competitive predictive performance and are computationally efficient to train and test, making them excellent candidates for r…
New random forest method provides optimal rates and confidence bands.
problem Improving random forest regression rates and constructing confidence bands.
method Proposed Ehrenfest centered purely random forests achieve optimal rates; used Gaussian approximation for supremum of empirical processes.
result Explicit asymptotic uniform confidence bands constructed for both random forest types.
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.
We propose random hinge forests, a simple, efficient, and novel variant of decision forests. Importantly, random hinge forests can be readily incorporated as a general component within arbitrary computation graphs that are optimized end-to-end with stochastic gradient descent or variants thereof. We derive random hinge…
Improved random forest proximities capture data geometry.
problem Inaccurate random forest proximities do not reflect learned data geometry.
method Introduce RF-GAP: Geometry- and Accuracy-Preserving proximities.
result RF-GAP improves geometric representation in tasks like data imputation.
Deep forests enhance expressiveness exponentially with depth, not width or tree size.
problem Understanding the role of depth, width, and tree size in deep forest performance.
method Provided upper and lower bounds on deep forest approximation complexity.
result Depth exponentially enhances deep forest expressiveness.
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.
This paper is a comment on the survey paper by Biau and Scornet (2016) about random forests. We focus on the problem of quantifying the impact of each ingredient of random forests on their performance. We show that such a quantification is possible for a simple pure forest , leading to conclusions that could apply more…
Forest-guided smoothing uses random forest outputs for interpretable local smoothers.
problem Creating interpretable local smoothers from complex random forest outputs.
method Uses random forest outputs to define spatially adaptive bandwidth matrices for a linear smoother.
result Improves interpretability and applicability of random forest outputs for various analyses.
In this paper we propose using the principle of boosting to reduce the bias of a random forest prediction in the regression setting. From the original random forest fit we extract the residuals and then fit another random forest to these residuals. We call the sum of these two random forests a \textit{one-step boosted …
A framework for the generation of bridge-specific fragility utilizing the capabilities of machine learning and stripe-based approach is presented in this paper. The proposed methodology using random forests helps to generate or update fragility curves for a new set of input parameters with less computational effort and…
By seeking the narrowest prediction intervals (PIs) that satisfy the specified coverage probability requirements, the recently proposed quality-based PI learning principle can extract high-quality PIs that better summarize the predictive certainty in regression tasks, and has been widely applied to solve many practical…
Improves time series classification with forest proximities.
problem Time series classification accuracy and efficiency.
method PF-GAP, an extension of RF-GAP proximities to proximity forests, combined with Multi-Dimensional Scaling and Local Outlier Factors.
result Forest proximities show stronger connection between misclassified points and outliers.
Random forests reduce bias and variance, especially in low SNR settings.
problem Reducing bias and variance in machine learning models, particularly in low SNR scenarios.
method Empirical study of random forests and bagging ensembles, focusing on the importance of mtry tuning. result Random forests reduce both bias and variance, outperforming bagging ensembles in high SNR settings.
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.
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.
Weighted SVM (or fuzzy SVM) is the most widely used SVM variant owning its effectiveness to the use of instance weights. Proper selection of the instance weights can lead to increased generalization performance. In this work, we extend the span error bound theory to weighted SVM and we introduce effective hyperparamete…
Online random forests improve Q-learning performance in specific gym environments.
problem Improving Q-learning performance in reinforcement learning tasks.
method Proposed online random forests as Q-function approximators and growing them as learning progresses.
result Improved performance over state-of-the-art Deep Q-Networks in specific gym environments.
New method learns representations for decision forests using input perturbation.
problem Decision forests struggle with raw structured data and lack effective representations.
method Approximate decision forest gradients through input perturbation.
result Effective representation learning for decision forests without structural changes.
Improved random forest models enhance machine learning predictions.
problem Equal weights for random forest base decision trees are not optimal.
method Proposes algorithms to modify weighting strategy of regular random forest.
result Numerical results show significant improvements over regular random forest.
Introduced by Breiman, Random Forests are widely used classification and regression algorithms. While being initially designed as batch algorithms, several variants have been proposed to handle online learning. One particular instance of such forests is the \emph{Mondrian Forest}, whose trees are built using the so-cal…
The study uses machine learning to predict cryptocurrency market trends and design profitable trading strategies.
problem Predicting cryptocurrency market trends for profitable trading.
method Applied k-Nearest Neighbours, eXtreme Gradient Boosting, and Random Forest classifiers to detect trends.
result High profit factor of 1.60 for unseen data, showing promising results.