A framework for sensitivity measures using scoring functions.
problem Constructing sensitivity measures for any elicitable functional.
method Score-based sensitivities constructed via consistent scoring functions.
result Demonstrated intuitive and desirable properties of score-based sensitivities.
Enhanced tree-based classifiers use derivatives and geometry for better function classification.
problem Improving classification of high-dimensional time series data.
method Integrates Functional Data Analysis with tree-based ensemble techniques, leveraging derivative and geometric features.
result Significant improvements over traditional approaches in function classification.
This paper explores ratio-based loss functions for machine learning.
problem Margin-based and distance-based loss functions for classification and regression.
method Investigation of ratio-based loss functions' properties.
result Proposed new ratio-based loss functions for regression.
Kernel-based function approximation improves reinforcement learning performance.
problem Average reward reinforcement learning in infinite horizon settings.
method Optimistic algorithm based on kernel ridge regression.
result No-regret performance guarantees and confidence intervals for kernel-based predictions.
New particle-based VI algorithm expands function class and improves scalability.
problem Limited function class in particle-based VI algorithms restricts flexibility and scalability.
method Introduces a functional regularization term to expand the function class and proposes PFG algorithm.
result Proposed PFG algorithm has larger function class, improved scalability, better adaptation to ill-conditioned distributions, and provable convergence.
A novel dictionary-based approach for predicting functions.
problem Functional-output regression with non-orthogonal dictionaries.
method Projection learning (PL) with reproducing kernel Hilbert spaces (KPL).
result KPL offers a flexible and computationally efficient solution.
Improved hypothesis testing and change-point detection using diffusion-based methods.
problem Limited power of score-based hypothesis tests and change-point detection.
method Extending score-based Fisher divergence to diffusion-divergence by multiplying score functions with a matrix-valued function or weight matrix.
result Theoretical quantification and demonstration of optimal performance of diffusion-based algorithms.
The paper proposes criteria and methods for evaluating and aggregating feature-based model explanations.
problem Lack of quantitative evaluation criteria for feature-based model explanations.
method Developed quantitative evaluation criteria (low sensitivity, high faithfulness, low complexity), devised a framework for aggregation, and derived a new aggregate Shapley value explanation function.
result A new aggregate Shapley value explanation function that minimizes sensitivity.
New tests for VaR and ES forecast encompassing using flexible link functions.
problem Testing forecast encompassing for Value at Risk and Expected Shortfall.
method Flexible link functions for testing convex forecast combinations and nonstandard asymptotic theory for boundary parameters.
result Tests based on new link functions outperform unrestricted linear link functions for one-step and multi-step forecasts.
We propose a new neural sequence model training method in which the objective function is defined by α-divergence. We demonstrate that the objective function generalizes the maximum-likelihood (ML)-based and reinforcement learning (RL)-based objective functions as special cases (i.e., ML corresponds to α→0 and R…
A machine learning method selects optimal orthonormal bases for functional data analysis.
problem Lack of formal criteria for choosing initial orthonormal bases in functional data methods.
method Proposes a machine learning algorithm to learn and place knots for efficient orthogonal spline bases (splinets).
result Demonstrates efficiency, especially for sparse functional data and complex physical systems.
New reward function improves GAIL performance in task-based environments.
problem Reward bias in adversarial imitation learning.
method Proposed a new reward function to overcome existing biases.
result New reward function outperforms existing methods in task-based environments.
Complexity measures for neural nets with general activations using path-based norms.
problem Control complexity of neural networks with arbitrary activation functions.
method Approximate general activations with ReLU networks and derive path-based norms for complexity control.
result Preliminary analyses of function spaces and regularized estimators.
A test for comparing function samples using MMD.
problem Testing if two functional data samples come from the same distribution.
method Maximum Mean Discrepancy (MMD) for functional data, with theoretical scaling analysis.
result The proposed test is effective and robust to functional reconstructions.
Enhances functional classifier performance with new tree-based methods and unbiased feature importance assessment.
problem Challenges of high-dimensional functional data and biased feature importance assessment.
method Augmented functional classification trees and random forests with ad-hoc conditional permutations for unbiased feature importance.
result Significant enhancement in predictive power of functional classifiers through new feature importance assessment.
Deep neural networks work well at approximating complicated functions when provided with data and trained by gradient descent methods. At the same time, there is a vast amount of existing functions that programmatically solve different tasks in a precise manner eliminating the need for training. In many cases, it is po…
In this paper we study nonconvex penalization using Bernstein functions whose first-order derivatives are completely monotone. The Bernstein function can induce a class of nonconvex penalty functions for high-dimensional sparse estimation problems. We derive a thresholding function based on the Bernstein penalty and di…
Recent state-of-the-art image segmentation algorithms are mostly based on deep neural networks, thanks to their high performance and fast computation time. However, these methods are usually trained in a supervised manner, which requires large number of high quality ground-truth segmentation masks. On the other hand, c…
Develops wavelet-based neural network approximation theory.
problem Analyzing neural network approximation capabilities over various activation functions.
method Wavelet frame theory on spaces of homogeneous type, sufficient conditions for approximation, error estimates.
result Derives sufficient conditions for neural networks to approximate any functions in a given space, including non-smooth activations.
New maximum score estimators using ReLU functions and deep neural networks.
problem Estimating parameters in models with sign restrictions.
method ReLU-based maximum score criterion and DNN architecture.
result RMS estimator achieves n−s/(2s+1) convergence rate and asymptotic normality. 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.
New analysis shows RPE-based Transformers can't approximate all functions.
problem Understanding the limitations of RPE-based Transformers in approximating continuous functions.
method Mathematical analysis and development of a novel attention module (URPE) to overcome limitations.
result RPE-based Transformers can't approximate all continuous sequence-to-sequence functions, even with depth and width.
Study expanding gradient Ricci solitons with Euclidean base.
problem Characterize expanding gradient Ricci solitons with specific properties.
method Analyze warped products with Euclidean base and invariant warping functions.
result Derive complete examples of expanding gradient Ricci solitons.
Improves graph-based active learning for non-Gaussian models.
problem Efficiently selecting data points for labeling in graph-based semi-supervised learning.
method Approximates non-Gaussian distributions, introduces rank-one update and model change acquisition function.
result Enhanced active learning for graph-based SSL under non-Gaussian models.
A new tree-based estimator, FastPD, efficiently estimates PD functions for machine learning models.
problem Efficiently estimating Partial Dependence functions for machine learning models.
method Proposes a new tree-based estimator, FastPD, to estimate PD functions.
result FastPD consistently estimates the desired population quantity and improves complexity from quadratic to linear.
Bandit algorithms have been predominantly analyzed in the convex setting with function-value based stationary regret as the performance measure. In this paper, motivated by online reinforcement learning problems, we propose and analyze bandit algorithms for both general and structured nonconvex problems with nonstation…
A key issue in the estimation of energy hedges is the hedgers' attitude towards risk which is encapsulated in the form of the hedgers' utility function. However, the literature typically uses only one form of utility function such as the quadratic when estimating hedges. This paper addresses this issue by estimating an…
A new algorithm for learning from functional data across multiple machines.
problem Handling large-scale functional data analysis.
method Distributed Gradient Descent Functional Learning (DGDFL) algorithm.
result First theoretical understanding and optimal learning rates for DGDFL.
Paper analyzes online reinforcement learning with outcome-based feedback, providing efficient algorithms and fundamental limits.
problem Assigning credit to actions in reinforcement learning with only endpoint rewards.
method Develops a provably sample-efficient algorithm for online reinforcement learning with general function approximation.
result Achieves O(CmcovH3/ε2) sample complexity, characterizing statistical separation between outcome-based and per-step rewards. A temporal point process is a mathematical model for a time series of discrete events, which covers various applications. Recently, recurrent neural network (RNN) based models have been developed for point processes and have been found effective. RNN based models usually assume a specific functional form for the time c…
Unified framework for Bayesian PDE-constrained inversion using physics-informed neural networks.
problem Incorporating prior distributions in function space into Bayesian PINN-based inversion.
method Functional-prior-based approaches (fpBPINN) to Bayesian PDE-constrained inversion using physics-informed neural networks (PINNs). Two complementary approaches: FPI-BPINN and fParVI-PINN.
result Accurate estimation of posterior distributions in seismic traveltime tomography and Darcy-flow permeability inversion.
We characterize Ricci almost solitons on semi-Riemannian warped products, considering the potential function to depend on the fiber or not. We show that the fiber is necessarily an Einstein manifold. As a consequence of our characterization we prove that when the potential function depends on the fiber, if the gradient…
Paper introduces a new method to identify brain hubs using both structural and functional connectivity.
problem Hub node identification in brain networks using only functional connectivity.
method Graph signal processing framework that models functional activity as graph signals on structural connectivity.
result The proposed GraFHub framework identifies hub nodes more accurately than conventional methods.
In this work, we propose new objective functions to train deep neural network based density ratio estimators and apply it to a change point detection problem. Existing methods use linear combinations of kernels to approximate the density ratio function by solving a convex constrained minimization problem. Approximating…
We develop a multi-kernel based regression method for graph signal processing where the target signal is assumed to be smooth over a graph. In multi-kernel regression, an effective kernel function is expressed as a linear combination of many basis kernel functions. We estimate the linear weights to learn the effective …
Introduces new performance measures using scaled utility functions.
problem Performance measurement in financial contexts.
method Certainty equivalents defined via scaled utility functions, well-posed portfolio optimization problem under generic conditions.
result Link between portfolio dynamics, benchmark process, and utility function choice in the long-run setting.
FuBIF enhances AD by using real-valued functions for more flexible anomaly detection.
problem Limitations of the Isolation Forest in adaptability and bias.
method Introduces FuBIF, a generalization of IF using real-valued functions for branching in evaluation trees.
result FuBIF significantly improves flexibility and evaluation tree construction.
The vicinal risk minimization (VRM) principle, first proposed by \citet{vapnik1999nature}, is an empirical risk minimization (ERM) variant that replaces Dirac masses with vicinal functions. Although there is strong numerical evidence showing that VRM outperforms ERM if appropriate vicinal functions are chosen, a compre…
In this letter, we derive the optimal discriminant functions for modulation classification based on the sampled distribution distance. The proposed method classifies various candidate constellations using a low complexity approach based on the distribution distance at specific testpoints along the cumulative distributi…
New method stabilizes IF-based estimators for causal mediation analysis with continuous mediators.
problem Stability issues in IF-based estimators for continuous mediators.
method Nonparametric weighted balancing method to estimate nuisance functions.
result Significant reductions in bias and variance compared to existing methods.
A new method for high-dimensional functional regression reduces multicollinearity and improves interpretability.
problem Multicollinearity, overfitting, and interpretability in high-dimensional functional linear models.
method Partition-based functional ridge regression framework.
result Improved numerical stability and enhanced interpretability without explicit variable selection.
Tree-based synthesis improves forecast accuracy in GDP and inflation.
problem Improving forecast accuracy in GDP and inflation.
method Developed a nonparametric synthesis function using regression trees.
result Tree-based synthesis leads to improved forecast accuracy.
Temporal Functional Circuits explain KAN forecasts with interpretable edge functions.
problem Lack of mechanistic explanations in KAN forecasting.
method Transform KAN edge functions into faithful, temporally grounded explanations using a gated residual KAN.
result Gated KAN achieves lower MSE than linear-only models on regime-switching signals.
SBBO optimizes complex spaces using sampling-based models.
problem Optimizing complex spaces with discrete variables.
method Simulation Based Bayesian Optimization (SBBO) using sampling-based surrogate models.
result Empirical effectiveness of SBBO in combinatorial optimization.
Constructs unique bases for CY varieties over valued fields.
problem Finding unique bases for CY varieties over valued fields.
method Uses techniques from higher rank degenerations in K-stability.
result Induces canonical functions on skeletons and agrees with tropicalizations of theta functions.
New neural network models for functional data.
problem Handling non-linear functional data.
method Functional Direct Neural Network (FDNN) and Functional Basis Neural Network (FBNN) with gradient-based optimization.
result Demonstrated effectiveness in complex functional models.
We propose a novel denoising framework for task functional Magnetic Resonance Imaging (tfMRI) data to delineate the high-resolution spatial pattern of the brain functional connectivity via dictionary learning and sparse coding (DLSC). In order to address the limitations of the unsupervised DLSC-based fMRI studies, we u…
Recently, neural networks trained as optimizers under the "learning to learn" or meta-learning framework have been shown to be effective for a broad range of optimization tasks including derivative-free black-box function optimization. Recurrent neural networks (RNNs) trained to optimize a diverse set of synthetic non-…