Inter-subject registration of cortical areas is necessary in functional imaging (fMRI) studies for making inferences about equivalent brain function across a population. However, many high-level visual brain areas are defined as peaks of functional contrasts whose cortical position is highly variable. As such, most ali…
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48 results for “functional regions”
sBayFDNN bridges deep learning and functional data analysis for complex, structured data.
problem Challenges in functional data analysis, especially for complex, continuously structured data.
method Sparse Bayesian functional deep neural network (sBayFDNN) that learns adaptive functional embeddings and interpretable region selection.
result First theoretical guarantees for a Bayesian deep functional model, ensuring reliability and statistical rigor.
Constructs non-asymptotic confidence regions for unknown functions in RKHS.
problem Global probabilistic confidence regions for unknown functions in RKHS.
method Reduces confidence region construction to estimating RKHS norm.
result Valid confidence regions can be constructed non-asymptotically.
The author studies regions foliated by 1D families of functions and their applications.
problem Understanding regions represented as foliated forms and natural smooth maps onto them.
method Investigates natural smooth maps respecting canonical projections and moment maps, focusing on foliated regions.
result Discusses the 1st derivative of functions and critical sets in foliated regions.
Employing profits data of Japanese companies in 2002 and 2003, we identify the non-Gibrat's law which holds in the middle profits region. From the law of detailed balance in all regions, Gibrat's law in the high region and the non-Gibrat's law in the middle region, we kinematically derive the profits distribution funct…
The paper identifies all link projections with isolate-region number one.
problem Determining link projections with a specific isolate-region number.
method Analyzing link projections to find isolated regions and their cardinality.
result All link projections with isolate-region number one are identified.
We show that for neural network functions that have width less or equal to the input dimension all connected components of decision regions are unbounded. The result holds for continuous and strictly monotonic activation functions as well as for the ReLU activation function. This complements recent results on approxima…
The paper improves confidence regions for band-limited functions using tighter norm bounds and majority voting.
problem Constructing reliable confidence regions for band-limited functions from noisy data.
method Improved norm bounds using Hoeffding's inequality and empirical Bernstein bound, majority voting to aggregate intervals.
result Confidence intervals retain their simultaneous coverage guarantee even when aggregated from random subsamples.
Previous work has questioned the conditions under which the decision regions of a neural network are connected and further showed the implications of the corresponding theory to the problem of adversarial manipulation of classifiers. It has been proven that for a class of activation functions including leaky ReLU, neur…
The paper develops methods for constructing confidence regions for regression functions in binary classification.
problem Building distribution-free confidence regions for regression functions in binary classification.
method Resampling test and empirical risk minimization approach for model classes with finite pseudo-dimensions and inverse Lipschitz parameterizations.
result Strong uniform consistency and exponential probably approximately correct bounds on the sizes of the regions.
Method constructs confidence regions for linear models with arbitrary predictors.
problem Constructing confidence regions for linear models with non-linear predictors.
method Mixed Integer Linear Programming for constraints.
result Empty confidence regions for hypothesis testing.
A Domain-Shrinking based Bayesian Optimization Algorithm with Order-Optimal Regret Performancestat.ML
Bayesian optimization algorithm reduces regret with efficient region pruning.
problem Sequential optimization of unknown functions in high-dimensional spaces.
method Gaussian process-based, domain shrinking through tree-based region pruning.
result Order-optimal regret performance with reduced computational complexity.
We investigate the complexity of deep neural networks (DNN) that represent piecewise linear (PWL) functions. In particular, we study the number of linear regions, i.e. pieces, that a PWL function represented by a DNN can attain, both theoretically and empirically. We present (i) tighter upper and lower bounds for the m…
Estimates the upper bound of linear regions in spheres centered at specific data points in ReLU neural networks.
problem Bounding the number of linear regions in specific areas of neural networks using ReLU activations.
method Developed a method to estimate the upper bound of linear regions in any sphere within the input space of a ReLU neural network.
result The boundaries of linear regions move away from training data points during training, and spheres centered at these points contain more regions than arbitrary points.
Tightening Fractional Covering Upper Bounds on the Partition Function for High-Order Region Graphscs.LG
In this paper we present a new approach for tightening upper bounds on the partition function. Our upper bounds are based on fractional covering bounds on the entropy function, and result in a concave program to compute these bounds and a convex program to tighten them. To solve these programs effectively for general r…
Modeling brain connectivity networks with graph-aware inference.
problem Pooling over functional regions loses information and independence assumptions are unreliable.
method Linear mixed effects model accounting for functional regions and edge dependence.
result Interpretable results comparing schizophrenics and healthy controls.
Paper develops a method to construct confidence regions for model parameters using batch means method.
problem Constructing confidence regions for model parameters in stochastic gradient descent.
method Batch means method to cancel out covariance matrix, using Polyak-Ruppert averaging.
result Established process-level functional central limit theorem for stochastic gradient descent estimators.
It is well-known that the expressivity of a neural network depends on its architecture, with deeper networks expressing more complex functions. In the case of networks that compute piecewise linear functions, such as those with ReLU activation, the number of distinct linear regions is a natural measure of expressivity.…
Conformal Prediction Regions match Imprecise Highest Density Regions under consonance.
problem Matching conformal prediction regions with highest density regions.
method Using consonance and the Imprecise Probability theory of clouds.
result Imprecise Highest Density Regions are equivalent to Conformal Prediction Regions under consonance.
This paper analyzes optimal stopping regions for American options with Poisson exercise opportunities.
problem Analyzing the optimal stopping regions for American options with Poisson exercise opportunities.
method Computing identities related to the first Poisson arrival time to an interval and applying them to the computation of the optimal strategies.
result Explicit expressions of the stopping and continuation regions and the value function are obtained.
The paper develops methods to estimate and assess the risk of binary classification.
problem Estimating the underlying regression function for binary classification.
method Three kernel-based semi-parametric resampling methods are proposed to build confidence regions for the regression function.
result The proposed methods guarantee regions with exact coverage probabilities and are strongly consistent.
Novel method for high-dimensional BO using CMA to define local regions.
problem Challenges in applying BO to high-dimensional optimization problems.
method CMA strategy to learn search distribution and define local regions.
result Our method outperforms existing techniques on various benchmarks.
RYU framework constructs safe regions for optimization problems.
problem Optimization problems with specific component functions.
method RYU framework for constructing safe regions.
result RYU framework improves upon state-of-the-art methods.
Functional connectivity refers to the temporal statistical relationship between spatially distinct brain regions and is usually inferred from the time series coherence/correlation in brain activity between regions of interest. In human functional brain networks, the network structure is often inferred from functional m…
Causal Analysis of the TOPCAT Trial: Spironolactone for Preserved Cardiac Function Heart Failurestat.ML
Causal analysis reveals regional discrepancies in TOPCAT trial results.
problem Inconclusive results in TOPCAT trial for heart failure treatment.
method Causal discovery methods with domain knowledge integration.
result Significant causal effects shown for some subgroups globally.
This work generalizes bounds on the number of linear regions in CPWL NNs.
problem Determining the number of linear regions in CPWL neural networks is challenging.
method Generalized bounds on the maximal number of linear regions for arbitrary CPWL activation functions.
result Depth significantly increases the number of linear regions, but not exponentially.
DNNs can approximate fractal functions with exponential linear regions.
problem Understanding neural network approximations of complex functions.
method Using Iterated Function Systems (IFS) and neural networks to generate fractal functions.
result DNNs can generate fractal functions with a number of linear regions exponential in the number of parameters.
We can compare the expressiveness of neural networks that use rectified linear units (ReLUs) by the number of linear regions, which reflect the number of pieces of the piecewise linear functions modeled by such networks. However, enumerating these regions is prohibitive and the known analytical bounds are identical for…
We analyze a reweighted version of the Kikuchi approximation for estimating the log partition function of a product distribution defined over a region graph. We establish sufficient conditions for the concavity of our reweighted objective function in terms of weight assignments in the Kikuchi expansion, and show that a…
The study examines the properties of linear regions in DNNs and how optimization techniques affect them.
problem Understanding the expressivity of deep neural networks through their linear regions.
method Empirical analysis of local properties of linear regions, including inspheres, hyperplane directions, decision boundaries, and surrounding regions.
result Different optimization techniques lead to distinct linear regions, even with similar classification accuracy.
We revisit the optimal investment and consumption problem with proportional transaction costs. We prove that both the value function and the slopes of the lines demarcating the no-trading region are analytic functions of cube root of the transaction cost parameter. Also, we can explicitly calculate the coefficients of …
The paper contains a short review of techniques examining regional wealth inequalities based on recently published research work but is also presenting unpublished features. The data pertains to Italy (IT), over the period 2007-2011: the number of cities in regions, the number of inhabitants in cities and in regions, a…
We study functions whose truncations are convex or quasiconvex.
problem Understanding functions with specific truncation properties.
method Analyzing -smooth functions with positive definite Hessians.
result Injectivity of restricted gradient in positive definite region.
Investigates consumption and investment strategies with preference for liquid assets.
problem Infinite horizon consumption-portfolio problem with liquid and illiquid risky assets.
method Analyzes properties of value function, categorizes solvency regions, and characterizes optimal policy.
result Liquidity preference leads to higher liquid wealth and lower consumption, potentially negative allocation to illiquid asset.
We give a geometrically intrinsic construction of a global time function for relatively compact diamond-shaped regions in arbitrary spacetimes. In the case of Minkowski spacetime, the flow of diffeomorphisms associated to a suitably normalized gradient of this time function becomes the conformal isotropy subgroup of th…
The paper develops optimal confidence regions for categorical data.
problem Constructing tight confidence regions for categorical data.
method Develops new theory for minimum average volume confidence regions.
result Shows optimality of the regions for categorical data and its implications for machine learning.
Bayesian optimization tackles constrained high-dimensional problems with penalties and trust regions.
problem Constrained optimization in high-dimensional black-box settings with expensive evaluations and complex feasibility regions.
method Penalty formulation, surrogate model, trust region strategy, Expected Improvement acquisition function.
result The proposed Trust Region method identifies high-quality feasible solutions with fewer evaluations and maintains stable performance.
The paper proposes a new model to capture specialized brain regions using mixture of regression experts.
problem Learning a forward mapping that relates stimuli to brain activation assumes all regions respond similarly, ignoring brain specialization.
method Clustering brain regions, learning different linear regression models for each cluster, using a mixture of linear experts.
result The proposed model predicts brain activation more accurately than conventional models.
The use of EEG biometrics, for the purpose of automatic people recognition, has received increasing attention in the recent years. Most of current analysis rely on the extraction of features characterizing the activity of single brain regions, like power-spectrum estimates, thus neglecting possible temporal dependencie…
We consider a generic configuration of regions, consisting of a collection of distinct compact regions in which may be either smooth regions disjoint from the others or regions which meet on their piecewise smooth boundaries in a generic way. We introduce a skeletal linking …
Method identifies regions of maximum dissimilarity in stochastic processes.
problem Comparing local characteristics of two random processes to find periods of maximum dissimilarity.
method Bayesian inference with integrated nested Laplace approximation for stochastic processes.
result Identifies regions of maximum dissimilarity with a certain volume.
Adaptive Replication Strategies in Trust-Region-Based Bayesian Optimization of Stochastic Functionsmath.OC
Adaptive replication improves stochastic function optimization.
problem Challenges in accurately estimating functions with high variance.
method Trust-region-based Bayesian optimization with adaptive replication.
result Adaptive replication substantially improves solution accuracy and efficiency.
DO-IQS: Dynamics-Aware Offline Inverse Q-Learning for Optimal Stopping with Unknown Gain Functionsstat.ML
DO-IQS recovers optimal stopping region from expert trajectories, addressing specific challenges.
problem Recovering optimal stopping region from expert trajectories with unknown gain functions.
method Dynamics-Aware Offline Inverse Q-Learning incorporating temporal information and confidence-based oversampling.
result Demonstrated performance on real and artificial data, including optimal intervention for critical events.
A neural network model minimizes region-based free energy for faster inference in MRFs.
problem Efficient inference in complex Markov random fields (MRFs).
method Region-based Energy Neural Network (RENN) that directly minimizes region-based free energy.
result RENN outperforms other methods in marginal distribution estimation, partition function estimation, and MRF learning.
Training-Time Batch Normalization Reshapes Local Partition Geometry in Piecewise-Affine Networkscs.LG
BN refines local partition geometry in piecewise-affine networks during training.
problem Understanding the effect of BN on the function realized during training in piecewise-affine networks.
method Analyzing the geometry of switching hyperplanes and affine-region partition conditioned on a mini-batch.
result BN increases expected local partition refinement in ReLU and piecewise-affine networks.
RAMs improve GAMs' accuracy by fitting components to subregions of feature space.
problem Subpar accuracy in GAMs due to inability to capture feature interactions.
method Identify subregions of feature space where interactions are minimized, fitting one component per subregion.
result RAMs offer improved expressiveness compared to GAMs while maintaining interpretability.
Develops an efficient approximation for full conformal prediction regions.
problem Computing exact full conformal prediction regions is computationally infeasible.
method Generates an approximate confidence region that can be efficiently computed.
result Introduces a new notion of thickness to quantify approximation tightness.
Article addresses practical challenges in conformal prediction.
problem Challenges in determining, computing, and controlling conformal prediction regions.
method Proposes a quadratic-polynomial non-conformity measure.
result Allows circumventing three challenges in full conformal prediction framework.