New method R-LOCO improves local feature importance analysis.
problem Local attribution methods fail to accurately identify important features.
method R-LOCO segments input space into regions and applies global methods within.
result R-LOCO delivers more accurate local attributions.
In this paper, we formulate a new local move on virtual knot diagram, called arc shift move. Further, we extend it to another local move called region arc shift defined on a region of a virtual knot diagram. We establish that these arc shift and region arc shift moves are unknotting operations by showing that any virtu…
Simple regional perturbations maintain model transferability while reducing adversarial example distortion.
problem Comparing efficacy of regional adversarial attacks without complex methods.
method Developed a simple regional adversarial perturbation attack using cross-entropy sign.
result Localized adversarial examples require significantly less Lp norm distortion compared to non-local counterparts. We introduce a local move on a link diagram named a region freeze crossing change which is close to a region crossing change, but not the same. We study similarity and difference between region crossing change and region freeze crossing change.
Combines global and local search for efficient global optimization with Gaussian processes.
problem Difficulties in building accurate GP models and getting stuck in suboptimal regions.
method Adopting AGLGP model combining global and local GP models, dividing space into regions, and switching between global and local searches.
result Efficiently locates the global optimum with benefits of both global and local search.
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…
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.
Bayesian framework for identifying localized regions of interest in dynamical systems.
problem Identifying regions of high-resolution uncertainty quantification in complex dynamical systems.
method Bayesian inference with Gaussian process surrogate and polynomial chaos expansion.
result Unified computational scheme reduces overall cost for uncertainty quantification.
Region crossing change is a local operation on link diagrams. The behavior of region crossing change on S2 is well understood. In this paper, we study the behavior of (modified) region crossing change on higher genus surfaces.
Pointwise localization allows more precise localization and accurate interpretability, compared to bounding box, in applications where objects are highly unstructured such as in medical domain. In this work, we focus on weakly supervised localization (WSL) where a model is trained to classify an image and localize regi…
Region crossing change is a local transformation on a knot or link diagram. We show that a region crossing change on a knot diagram is an unknotting operation, and we define the region unknotting numbers for a knot diagram and a knot.
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.
Proposes a method to learn system dynamics and region of attraction from trajectories.
problem Learning accurate dynamics and region of attraction from system trajectories.
method Uses local stability information as a prior to learn vector field and region of attraction.
result Efficient sampling and accurate estimate of dynamics in inner approximation of region of attraction.
Localized SVMs maintain SVM's consistency properties for large datasets.
problem Inefficient computational requirements of global SVMs for large data sets.
method Localized SVMs apply different hyperparameters to different regions of the input space.
result Localized SVMs inherit Lp- and risk consistency from global SVMs. Deep ReLU networks with extra parameters have mostly good loss landscapes.
problem Finding good local minima in the loss landscape of deep neural networks.
method Analyzing shallow and deep ReLU networks with extra parameters on a generic dataset.
result Most activation patterns correspond to regions with no bad local minima.
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.
MD-split+ creates locally valid prediction regions for complex data.
problem Localized prediction regions for complex data.
method Localized model performance-based partitioning of feature space X.
result MD-split+ creates valid prediction regions that scale to high dimensions.
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.
RbX generates local explanations for black-box models using greedy polytope construction.
problem Generating interpretable local explanations for complex models.
method Greedy algorithm for building a convex polytope to approximate feature regions.
result RbX can more accurately identify important features compared to existing methods.
New GP model estimates piecewise continuous functions.
problem Piecewise continuous regression functions in scientific and engineering applications.
method Local Gaussian process model with partitioned local data and joint estimation of boundaries.
result Superior performance over conventional GP models in estimating piecewise regression functions.
Locally isoperimetric partitions minimize perimeter in space.
problem Finding minimal perimeter partitions in space.
method Proving closure theorem to limit sequences of isoperimetric clusters.
result Examples of isoperimetric partitions in various dimensions.
To collectively forecast the demand for ride-sourcing services in all regions of a city, the deep learning approaches have been applied with commendable results. However, the local statistical differences throughout the geographical layout of the city make the spatial stationarity assumption of the convolution invalid,…
New models reduce regional inequality by adjusting exchange range and asset distribution bias.
problem Reduction of regional inequality in economic systems.
method Proposed new asset exchange models with spatial exchange range and local support bias to adjust asset distribution and circulation rates.
result Achieved asset distribution from over-concentration to exponential and eventually normal, reducing Gini coefficient.
Proves conditions for separating regions in homogeneous spaces without trivial topology.
problem Separating regions in homogeneous, locally compact spaces without trivial topology.
method Analyzes properties of closed subsets and their boundaries in Čech cohomology.
result Conditions for irreducible separation without trivial topology.
Spatial graphs of non-Eulerian or proper Eulerian planar graphs are unknottable by region crossing changes.
problem Unknottability of spatial graphs by region crossing changes.
method Region crossing changes to switch over/under relations within regions of spatial graph diagrams.
result Spatial graphs of non-Eulerian or proper Eulerian planar graphs are unknottable by region crossing changes.
Improves arc separation result for homogeneous spaces.
problem Separating regions in homogeneous spaces by arcs.
method Using homogeneity instead of strong local homogeneity, and considering arcs with one interior point.
result Regions in homogeneous spaces of dimension ≥ 2 are not separated by arcs.
The expectation-maximization (EM) algorithm has been widely used in minimizing the negative log likelihood (also known as cross entropy) of mixture models. However, little is understood about the goodness of the fixed points it converges to. In this paper, we study the regions where one component is missing in two-comp…
Proposes sparse local and regional counterfactual rules for robust recourses.
problem Challenges in counterfactual explanations, especially stability, synthesis, and implementation.
method Probabilistic framework using Random Forest to derive sparse local and regional counterfactual rules.
result Effective recourses derived from high-density regions, providing sparse and robust counterfactual rules.
AdaScale-TuRBO improves high-dimensional Bayesian optimization by dynamically scaling the GP lengthscale.
problem Inappropriate lengthscale design in TuRBO's local GP model causes suboptimal performance in high dimensions.
method Proposes AdaScale-TuRBO, which scales the GP lengthscale with both problem dimension and trust region size.
result AdaScale-TuRBO robustly outperforms standard TuRBO and other methods on synthetic and real-world tasks.
SOCP uses SOM to find groups and local calibration buffers for better regional coverage.
problem Heterogeneous regional coverage gaps in conformal prediction.
method Self-Organizing Map (SOM) for group discovery; local calibration buffers at BMU or fixed grid.
result Reduces regional coverage gaps on 7/8 benchmarks by 7.1%.
Geotagged data can be used to describe regions in the world and discover local themes. However, not all data produced within a region is necessarily specifically descriptive of that area. To surface the content that is characteristic for a region, we present the geographical hierarchy model (GHM), a probabilistic model…
New method detects and locates changes in spatio-temporal point processes.
problem Detecting and localizing changes in spatio-temporal data.
method Score-based, likelihood-free approach estimating change time and region.
result The method provides theoretical guarantees on detection and localization accuracy.
Gradient-based methods find saddle points, not critical points, in neural networks.
problem Gradient-based optimization methods converge to saddle points rather than critical points in deep neural networks.
method Critical point-finding methods used to analyze neural network losses.
result Gradient-based methods often converge to or pass through gradient-flat regions, where gradient norm has a stationary point.
We establish some a priori geometric relations on stable minimal surfaces lying inside three-manifolds with scalar curvature uniformly bounded below. The relations are based on a slight generalization of a formula due to Castillon. We apply it to prove non-local rigidity results in the particular sense that they expres…
The paper introduces a method for fitting complex models using simulation and optimization.
problem Fitting models with intractable likelihood or moments.
method Sequential sampling and local smoothing, combining global and local search phases.
result The proposed method outperforms alternative approaches in fitting complex models.
A new method for multiclass calibration using vector quantization.
problem Challenges in multiclass calibration, especially in high-stakes settings.
method Compositional approach via Vector Quantization (VQ) to learn region-specific calibration maps.
result Significant improvements in local calibration with competitive global calibration and predictive performance.
BO limits search to lower dimensions with LGPR, improving efficiency and accuracy.
problem High computational costs in BO for high-dimensional optimization.
method Limits search region to lower dimensions and uses LGPR for local Gaussian process regression.
result Search efficiencies improved by about 69% and 40% for Ackley and Rosenbrock functions.
Proposes a continuous, differentiable model from local adaptive models.
problem Inadequate continuity and differentiability in over-parameterized models.
method A global continuous and differentiable model constructed from weighted averages of locally learned models.
result Achieves faster statistical convergence and improved performance in various settings.
Efficiently checks local robustness in neural networks using geometric projections.
problem Ensuring robustness of neural networks against adversarial inputs.
method Systematic search for decision boundaries in convex polyhedral regions using geometric projections.
result Shows geometric projections can efficiently check robustness in neural networks.
Multiple sclerosis (MS) is an inflammatory demyelinating disease of the central nervous system (CNS) that results in focal injury to the grey and white matter. The presence of white matter lesions biases morphometric analyses such as registration, individual longitudinal measurements and tissue segmentation for brain v…
Dynamic Ensemble Selection (DES) techniques aim to select locally competent classifiers for the classification of each new test sample. Most DES techniques estimate the competence of classifiers using a given criterion over the region of competence of the test sample (its the nearest neighbors in the validation set). T…
DCSO dynamically selects top-performing base detectors for outlier ensembles.
problem Challenges in selecting and combining outlier scores from different detectors.
method DCSO dynamically selects top-performing base detectors based on local k-nearest neighbors.
result DCSO provides consistent performance improvement over static combination approaches.
In this thesis, we consider domino tilings of three-dimensional regions, especially those of the form D×[0,N]. In particular, we investigate the connected components of the space of tilings of such regions by flips, the local move performed by removing two adjacent dominoes and placing them back in t…
In this paper, we consider domino tilings of regions of the form D×[0,n], where D is a simply connected planar region and n∈N. It turns out that, in nontrivial examples, the set of such tilings is not connected by flips, i.e., the local move performed by removing two adjace…
Localized uncertainty attacks target uncertain regions to create imperceptible adversarial examples.
problem Adversarial examples that are imperceptible to humans and strong under deterministic classifiers.
method Localized uncertainty attacks by perturbing uncertain regions, using predictive uncertainty or surrogate models.
result Localized uncertainty attacks produce strong adversarial examples that retain input similarity.
We target the problem of finding a local minimum in non-convex finite-sum minimization. Towards this goal, we first prove that the trust region method with inexact gradient and Hessian estimation can achieve a convergence rate of order O(1/k2/3) as long as those differential estimations are sufficientl…
One of the founding paradigms of machine learning is that a small number of variables is often sufficient to describe high-dimensional data. The minimum number of variables required is called the intrinsic dimension (ID) of the data. Contrary to common intuition, there are cases where the ID varies within the same data…
Proposes methods for local clustering in attributed graphs.
problem Finding a single cluster concentrated on a specific region in a graph.
method Introduces Graph Unimodality (GU) and Attribute Unimodality (AU) measures, and LOCLU algorithm to optimize Compactness score.
result Local cluster detected by LOCLU concentrates on the region of interest and exhibits unimodal data distribution.