Study centers of convex polyhedrons that are independent of parameters.
problem Characterize centers of convex polyhedrons that are independent of parameters.
method Investigate centers defined by Riesz potential and Poisson's integral, providing necessary and sufficient conditions for independence.
result Necessary and sufficient condition for existence of centers independent of parameters.
Study shows priors are crucial for accurate causal learning from unlabeled data.
problem Improving causal learning from unlabeled data.
method Investigated causal learning using Bayesian methods and analyzed the impact of priors.
result Factorized priors lead to factorized posteriors, aligning with independent causal mechanisms.
New MRI method maps tissue parameters more accurately by ignoring voxel independence.
problem Voxel independence assumption limits model fitting reliability and repeatability.
method Self-supervised deep variational approach with Gaussian mixture prior.
result Our method outperforms current techniques in dMRI simulations and real data.
Gaffke's bound is optimal for a specific parameter ordering in independent random vectors.
problem Finding optimal lower confidence bounds for a scalar parameter in independent random vectors.
method Revisiting classical work on lower confidence bounds, specializing to independent components, and proving optimality with respect to a specific parameter ordering.
result Gaffke's bound is Buehler optimal for the maximum marginal mean parameter.
Deep learning models predict generalization gaps without specific task or architecture.
problem Predicting when deep learning works across different tasks and architectures.
method Created a dataset of 13,500 neural networks trained on various spiral datasets and parameters. Used this dataset to train predictors for generalization gaps.
result DNNs and RNNs outperform linear models in predicting generalization gaps, with RNNs achieving R2=0.584. Type system captures CI relationships for probabilistic models.
problem Challenges in inference for models with mixed discrete and continuous parameters.
method Information flow type system for probabilistic programming.
result Well-typed programs guarantee certain CI relationships.
Develops methods for constructing likelihoods and priors for Bayesian networks.
problem Learning parameters and structure of Bayesian networks from limited data.
method Introduces assumptions for constructing likelihoods and priors from small assessments.
result Allows construction of likelihoods and priors for a wide range of network structures.
We generalize the classical Lie results on a basis of differential invariants for a one-parameter group of local transformations to the case of arbitrary number of independent and dependent variables. It is proved that if universal invariant of a one-parameter group is known then a complete set of functionally independ…
Improved sample complexity bounds for neural networks with depth independence.
problem Understanding the sample complexity of neural networks with depth and size independence.
method New bounds on Rademacher complexity with norm constraints on parameter matrices.
result Improved sample complexity bounds that are fully independent of network size under certain assumptions.
Constructs initial data for multiple black holes with specified ADM parameters.
problem Forming multiple black holes with specific ADM parameters.
method Smooth, asymptotically flat vacuum initial data with prescribed ADM energy, momentum, and angular momentum.
result Maximal development of data results in spacetimes containing multiple black holes.
The paper characterizes measures preserving independence through planar web geometry.
problem Characterizing measures with preserved independence.
method Planar web geometry and inhomogeneous Abelian functional equations.
result The independence-preserving property is preserved by coordinatewise reparametrizations and forms a natural invariant.
Bayesian neural networks learn graph structure with interpretable parameters.
problem Learning graph structure from nodal observations in data with uncertainty.
method Introduces novel iterations with independently interpretable parameters and Bayesian neural networks.
result Bayesian neural networks provide well-calibrated uncertainty quantification on graph structure.
The study reveals a persistent bias in the distribution of holonomy on compact hyperbolic 3-manifolds.
problem The distribution of holonomy on compact hyperbolic 3-manifolds is not uniformly distributed.
method An asymptotic count of closed geodesics by their length and holonomy, and analysis of spectral parameters.
result A normalized, smoothed bias count of holonomy is distributed according to a probability distribution, controlled by the number of zero spectral parameters.
Graph neural networks often assume vertex labels are independent, but we show this is rarely true and propose a method to improve predictions.
problem Graph neural networks often assume vertex labels are conditionally independent given their neighborhood features, which is rarely true.
method We model the joint distribution of residuals on vertices with a parameterized multivariate Gaussian and estimate parameters by maximizing the marginal likelihood of the observed labels.
result Our method achieves substantially higher accuracy than competing baselines and can be interpreted as the strength of correlation among connected vertices.
New algorithms improve ICA performance without manual tuning.
problem Improving Independent Component Analysis (ICA) performance.
method Developed majorization-minimization framework for non-convex loss function.
result Stochastic algorithms guarantee loss function decrease at each iteration.
Proves generic independence and additivity of SL(2,C) Casson-Lin invariant.
problem SL(2,C) Casson-Lin invariant's parameter dependence and additivity under knot sums.
method Topology, microlocal analysis, algebraic geometry, Behrend functions.
result Generically independent and additive invariant under knot sums.
LoRA-Curve connects independent LoRA optima through continuous low-loss valleys, improving Bayesian model averaging.
problem Challenges in estimating epistemic uncertainty in LoRA-based Bayesian inference.
method Introduces LoRA-Curve, a segmented Bézier curve parameterization in the LoRA space, with free and anchored configurations.
result Empirically shows that connecting independent LoRA optima through continuous low-loss valleys improves mutual information of the predictive distribution.
Model estimates lung well-aerated volume from CT images, independent of patient and imaging parameters.
problem Lack of clear connection between quantitative metrics in lung CT images and physiology.
method Patient-independent model using Gaussian fit to lower CT histogram data points.
result Model estimates well-aerated volume (WAVE) independent of CT reconstruction parameters and respiratory cycle.
We show that the only parameter prior for complete Gaussian DAG models that satisfies global parameter independence, complete model equivalence, and some weak regularity assumptions, is the normal-Wishart distribution. Our analysis is based on the following new characterization of the Wishart distribution: let W be an …
The group membership prediction (GMP) problem involves predicting whether or not a collection of instances share a certain semantic property. For instance, in kinship verification given a collection of images, the goal is to predict whether or not they share a {\it familial} relationship. In this context we propose a n…
This Ph.D. thesis is devoted to the constructions of Lagrangian formulation on Finsler and Kawaguchi manifolds. While Finsler geometry is a natural extension of Riemannian geometry, Kawaguchi geometry is the extension of Finsler geometry to higher order derivatives and to k-dimensional parameter space. The latter exten…
Approach uses machine learning to identify structural modal parameters from output-only data.
problem Identifying modal parameters from output-only data for structural health monitoring.
method Unsupervised learning using a self-coding deep neural network to separate modal responses from vibration data.
result The approach effectively identifies structural modal parameters from system responses.
We develop and apply an approach for analyzing multi-curve data where each curve is driven by a latent state process. The state at any particular point determines a smooth function, forcing the individual curve to switch from one function to another. Thus each curve follows what we call a switching nonparametric regres…
A new VAE approach solves inverse problems without explicit inverse mapping.
problem Solving inverse problems without explicit inverse mapping.
method Discarding the encoder in VAE architecture, directly optimizing latent variables.
result The latent variables can exhibit mutually independent properties without an encoding process.
Unified framework connects two market-making models, revealing their underlying equivalence.
problem Independent calibration of two market-making frameworks (Avellaneda-Stoikov and Cartea-Jaimungal).
method Axiomatic approach to market preference functional, showing equivalence under specific conditions.
result Avellaneda-Stoikov and Cartea-Jaimungal frameworks are equivalent under certain conditions.
We propose a novel approach for nonlinear regression using a two-layer neural network (NN) model structure with sparsity-favoring hierarchical priors on the network weights. We present an expectation propagation (EP) approach for approximate integration over the posterior distribution of the weights, the hierarchical s…
Log-linear models are the popular workhorses of analyzing contingency tables. A log-linear parameterization of an interaction model can be more expressive than a direct parameterization based on probabilities, leading to a powerful way of defining restrictions derived from marginal, conditional and context-specific ind…
The discovery of non-linear causal relationship under additive non-Gaussian noise models has attracted considerable attention recently because of their high flexibility. In this paper, we propose a novel causal inference algorithm called least-squares independence regression (LSIR). LSIR learns the additive noise model…
A new test for conditional independence in discretized data.
problem Testing conditional independence when only discretized observations are available.
method Proposes a conditional independence test designed for discretized observations, using bridge equations to recover latent variables' information.
result Demonstrates the effectiveness of the proposed test through theoretical and empirical validation.
New method tracks time-varying parameters in data.
problem Tracking unknown time-varying parameters in data.
method Stochastic gradient descent-based recursive scheme with log-likelihood as gain function.
result Convergence in mean-square error in a suitable neighborhood of the unknown parameter.
New algorithms improve learning of long-term actions in reinforcement learning.
problem Violation of parameter independence assumption in deep function approximation.
method Reconsidered option-critic and hierarchical option-critic training for deep settings.
result Significantly improved stability and faster convergence in Atari games.
Study algebraic relations of Vassiliev invariants for families of knots.
problem Understanding algebraic structure of Vassiliev invariants for knot families.
method Analyzing algebraic relations and generating sets of Vassiliev invariants in 3D Chern-Simons theory.
result For 1-parametric knot families, Vassiliev invariants are finitely generated. For more parameters, there can be an infinite number of generators.
This research designs a data-driven partition to test independence between continuous variables.
problem Testing independence between continuous random variables.
method Empirical log-likelihood statistic and data-driven tree-structured partition.
result Strongly consistent test of independence over probability families.
Paper introduces new regression methods for consistent estimation of biophysical parameters.
problem Estimating biophysical parameters while respecting auxiliary variables.
method Linear and nonlinear kernel-based regression models with consistency constraints.
result Models provide closed-form solutions and successfully estimate chlorophyll content.
The study analyzes the convergence rates of Gaussian mixtures of experts.
problem Analyzing the convergence rates of Gaussian mixtures of experts.
method The study uses a novel notion of algebraic independence and optimal transport theory to establish convergence rates and minimax lower bounds.
result The study provides theoretical convergence rates for maximum likelihood estimation of over-specified Gaussian mixtures of experts.
A new method for CI construction from nuisance parameter estimators.
problem Building confidence intervals from nuisance parameter estimators.
method Collaborative TMLE (C-TMLE) for inference.
result The C-TMLE yields a CI under certain conditions.
The extension of the classical Bayesian penalized spline method to inference on vector-valued functions is considered, with an emphasis on characterizing the suitability of the method for general application.We show that the standard quadratic penalty is exactly analogous to the energy of a stretched string, with the p…
Derives PDEs from data using manifold learning and neural networks.
problem Identifying PDEs from unknown variables and dynamics.
method Combines manifold learning (Diffusion Maps) and neural networks.
result Emergent space identification connects with multiscale computation.
Considering the kinematics of the moving frame associated with a constant mean curvature surface immersed in S^3 we derive a linear problem with the spectral parameter corresponding to elliptic sinh-Gordon equation. The spectral parameter is related to the radius R of the sphere S^3. The application of the Sym formula …
Improved batch-size independent regret bounds for nonlinear reward functions.
problem Nonlinear reward functions in combinatorial multi-armed bandit problems.
method Introducing Gini-weighted smoothness to account for both nonlinearity and concentration properties of arms.
result Achieved dramatic improvements in upper bounds for the probabilistic maximum coverage problem.
NKN deep neural network learns governing equations and classifies images.
problem Learning governing equations and classifying images with deep neural networks.
method Nonlocal kernel network (NKN) that is resolution independent, deep, and handles various tasks.
result NKN outperforms baseline methods in learning governing equations and image classification tasks.
New findings on Malgrange-Galois groupoid for Painlevé VI equation parameters.
problem Understanding transformations preserving specific forms for Painlevé VI equation.
method Computed Malgrange-Galois groupoid for Painlevé VI family with all parameters.
result Solutions of Painlevé VI do not satisfy new partial differential equations.
New ICA method exploits sparsity for better brain imaging analysis.
problem ICA's independence assumption is too strict for real-world data.
method Entropy bound minimization with sparsity exploitation.
result Improved ICA performance through direct incorporation of sparsity.
Deep ReLU networks generalize well with few parameters.
problem Generalization of overparametrized deep neural networks.
method Explicit bounds on test error independent of overparametrization and VC dimension.
result Generalization error is independent of network architecture and overparametrization.
Gaussian kernel tests are optimal against smooth alternatives.
problem Understanding the statistical properties of nonparametric tests using Gaussian kernels.
method Analysis of Gaussian kernel-based goodness-of-fit, homogeneity, and independence tests.
result Gaussian kernel tests are minimax optimal against smooth alternatives in all three settings.
New AI-block models for clustering high-dimensional variables based on maxima of random processes.
problem Clustering high-dimensional variables with weakly dependent maxima of random processes.
method Asymptotic Independent block (AI-block) models and an algorithm for variable clustering.
result The proposed AI-block models and algorithm can effectively identify clusters in high-dimensional data.
We give a new, very general, formulation of the compressed sensing problem in terms of coordinate projections of an analytic variety, and derive sufficient sampling rates for signal reconstruction. Our bounds are linear in the coherence of the signal space, a geometric parameter independent of the specific signal and m…
We prove that if the Black-Scholes formula holds with the spot volatility for call options with all strikes, then the volatility parameter is constant. The proof relies some result on semimartingales (Theorem 2) of independent interest.