A new method tests conditional independence by transforming it into an unconditional problem using transport maps.
problem Testing conditional independence between two random vectors given a third.
method Constructing transport maps to transform conditional independence into unconditional independence, estimating these maps from data using conditional continuous normalizing flow models.
result The proposed method is validated through simulations and real-data analysis, demonstrating practical effectiveness.
Discrete hyperbolic isometries proven via test maps.
problem Proving discreteness of hyperbolic isometries.
method Using test maps to show discreteness of subgroups.
result Zariski dense subgroups are discrete under certain conditions.
Deep CITs test conditional independence in images, improving brain MRI scan analysis.
problem Testing conditional independence in complex, high-dimensional variables like images.
method Combines embedding maps and nonparametric CITs for feature representations.
result Valid DNCITs for brain MRI scans and behavioral traits, confirming null results.
Novel approach uses neural networks to enhance CI testing for feature selection.
problem Challenges in implementing Markov blanket feature selection due to CI testing limitations.
method Two-step approach: feature mapping followed by CI testing using k-NN. result The method boosts CI testing performance, leading to improved feature selection.
Let SL(2, H) be the group of 2×2 quaternionic matrices A=(acbd) with quaternionic determinant detA=∣ad−aca−1b∣=1. This group acts by the orientation-preserving isometries of the five dimensional (real) hyperbolic space. We obtain discreteness criteria f…
Paper tackles efficient exploration of unseen graph-structured environments.
problem Efficient exploration of unseen graph-structured environments.
method Learning to explore framework using reinforcement learning and graph-structured memory.
result Approach outperforms hand-engineered methods in software testing and real-world applications.
Characterizes test error in learning with deep, structured feature maps.
problem Characterizing test error in learning with deep, structured feature maps.
method Asymptotic analysis of feature covariance and population covariance.
result Closed-form formula for feature covariance in Gaussian rainbow neural networks.
Two modified tests improve the reliability of evaluating explanation methods.
problem Methodological concerns in evaluating explanation methods for saliency maps.
method Proposed modifications to the Model Parameter Randomisation Test (MPRT): Smooth MPRT and Efficient MPRT.
result Enhanced metric reliability, facilitating more trustworthy deployment of explanation methods.
We find a deterministic equivalent for random feature regression's test error, independent of feature map dimension.
problem Understanding the generalization performance of random feature ridge regression.
method We derive a deterministic equivalent for the test error of RFRR under a concentration property, showing it can be approximated by a closed-form expression dependent on feature map eigenvalues.
result Our approximation guarantee is non-asymptotic, multiplicative, and independent of the feature map dimension, providing a tight result for the smallest number of features achieving optimal minimax error rate.
A new framework for brain mapping using statistical agnostic methods.
problem Estimating brain connectivity with limited data and controlling false positives.
method Statistical Agnostic Mapping (SAM) based on concentration inequalities.
result Relieves instability and provides less conservative p-value correction.
Study validates saliency maps of GNNs using selective inference.
problem Reliability of GNN saliency maps in graph-structured data.
method Statistical testing framework with selective inference to control Type I error rate.
result Valid p-values for salient subgraphs, ensuring meaningful information. LM-SNNs use lattice maps to classify and cluster images.
problem Image classification and clustering.
method Lattice map spiking neural networks with cooperative and competitive interactions, inhibition strategies, and biologically motivated learning rules.
result LM-SNNs effectively classify and cluster images using self-organized filters.
Implicit models can match or exceed explicit models with more test-time compute.
problem Understanding the expressive power and scaling of implicit models.
method Nonparametric analysis of expressive power, mathematical characterization of implicit operators, and test-time scaling experiments.
result Implicit models can progressively express more complex mappings through iteration, matching a richer function class with test-time compute.
This work explains GAN mode collapse and convergence issues via optimal transportation theory.
problem GANs struggle with convergence and mode collapse due to discontinuous optimal transportation mappings.
method The study connects GANs to optimal transportation theory, testing hypotheses about discontinuity and proposing a new method to approximate continuous Brenier potentials.
result The supports of real data distributions are often non-convex, leading to discontinuous optimal transportation mappings and mode collapse in GANs.
Visualizes ConvNets without confounding effects.
problem Misinterpretation of saliency maps due to confounding variables.
method Univariate statistical tests and partial back-propagation to remove confounding effects.
result Visualization of confounder-free saliency maps.
Neural network outperforms traditional methods in chaotic dynamics classification.
problem Classifying chaotic and regular dynamics of the Chirikov standard map.
method Trained a convolutional neural network on finite-length trajectories compared to traditional Lyapunov exponent computation.
result Neural network outperforms traditional methods for short periods, converging faster and more robustly.
Novel algorithm solves optimal transport using evolving probability distributions and convolution.
problem Sample-based optimal transport problem.
method Adversarial formulation with convolution of adaptive kernel and evolving measure.
result Algorithm robust to dimensionality and produces complex maps.
Deep neural networks improve two-sample testing.
problem Efficiently distinguishing between two unknown distributions.
method Deep learning representations for two-sample testing.
result Significant reduction in type-2 error rate compared to existing methods.
New method uses UAV imagery and ML to map crops and weeds.
problem Mapping crops and weeds at high resolution.
method Machine Learning algorithms trained on expert-masked images.
result Maps with >90% identification efficiency at 5m altitude.
New neural networks learn mappings between probability measures and functions.
problem Learning mappings between Wasserstein space of probability measures and function spaces.
method Two types of neural networks: bin density and cylindrical approximation, are proposed and supported by universal approximation theorems.
result Accuracy and efficiency of mean-field neural networks in generalization error with various test distributions.
Study characterizes training and test risks for MAP regression with Gaussian priors.
problem Understanding high-dimensional behavior of regularized linear regression with informative priors.
method Maximum a posteriori (MAP) regression with Gaussian priors, using random matrix theory.
result Closed-form risk formulas reveal the bias-variance-prior tradeoff and explain double descent.
New tests for binary classification regression functions without distribution assumptions.
problem Testing regression functions in binary classification without distributional assumptions.
method Conditional kernel mean embeddings and resampling-based framework.
result Distribution-free hypothesis tests with exact type I error control.
Deep-learning method improves hypothesis testing for independence.
problem Improving hypothesis testing for independence using deep learning.
method Proposes deep-testing, a novel procedure that uses a deep neural network to distinguish between data generated under and outside a given statistical model.
result Deep-testing achieves the highest overall power against nineteen competing methods across various dependence structures.
A new method improves robustness in image translation by modeling uncertainty.
problem Performance degradation in image translation models due to lack of robustness to outliers and uncertainty.
method UGAC method based on Uncertainty-aware Generalized Adaptive Cycle Consistency, modeling per-pixel residual with generalized Gaussian distribution.
result Our method exhibits stronger robustness towards unseen perturbations in test data.
The study evaluates saliency metrics for image classifier outputs, finding inconsistencies and unreliability.
problem Inconsistencies and unreliability in saliency metrics for evaluating pixel relevance.
method Investigated existing saliency metrics, calculated and compared their consistency, and applied psychometric testing methods.
result Saliency metrics can be statistically unreliable and inconsistent, affecting comparative rankings.
Generalizes Newmark methods for nonholonomic systems.
problem Energy behavior in nonholonomic systems.
method Nonholonomic exponential map to generalize Newmark methods.
result Composition of two Newmark methods can improve energy behavior.
The diagnosis of Alzheimer's disease (AD) in routine clinical practice is most commonly based on subjective clinical interpretations. Quantitative electroencephalography (QEEG) measures have been shown to reflect neurodegenerative processes in AD and might qualify as affordable and thereby widely available markers to f…
VDTW improves cross-year crop mapping accuracy.
problem Cross-year crop mapping accuracy is poor with existing methods.
method Vector Dynamic Time Warping (VDTW) for multi-year classification.
result VDTW achieves 99.85% and 99.74% overall accuracies for same and cross years, respectively.
Balanced Activation improves object detection performance on long-tailed datasets.
problem Mismatch between training and testing label distributions in object detection.
method Introduces Balanced Activation (Balanced Softmax and Balanced Sigmoid) to address label distribution shift.
result Balanced Activation provides ~3% gain in mAP on LVIS-1.0 compared to state-of-the-art methods.
The problem of attempting to learn the mapping between data and labels is the crux of any machine learning task. It is, therefore, of interest to the machine learning community on practical as well as theoretical counts to consider the existence of a test or criterion for deciding the feasibility of attempting to learn…
In this article we relate two different densities. Let Fk be the free group of finite rank k≥2 and let α be the abelianization map from Fk onto Zk. We prove that if S⊆Zk is invariant under the natural action of SL(k,Z) then the asymptotic density of S in $\…
Approximating non-linear kernels using feature maps has gained a lot of interest in recent years due to applications in reducing training and testing times of SVM classifiers and other kernel based learning algorithms. We extend this line of work and present low distortion embeddings for dot product kernels into linear…
New method uncovers global topology through local interactions, reducing algorithm complexity.
problem Global interaction is necessary for forming feature maps that preserve global topology.
method Competing agents engage in local interactions to form feature maps without global interaction.
result Local interactions can uncover global topology, leading to consistent map quality across diverse datasets.
We introduce a new methodology for forecasting which we call Signal Diffusion Mapping. Our approach accommodates features of real world financial data which have been ignored historically in existing forecasting methodologies. Our method builds upon well-established and accepted methods from other areas of statistical …
ECCIT improves conditional independence tests by calibrating for miscalibration.
problem Inaccurate frequentist guarantees in CITs, especially in small samples and misspecified models.
method Empirically Calibrated Conditional Independence Tests (ECCIT) that optimize and correct for miscalibration.
result ECCIT achieves valid FDR with higher power than existing calibration strategies.
Develops a two-sample test using projected Wasserstein distance to handle high-dimensional data.
problem Testing whether two high-dimensional samples come from the same distribution.
method Optimal projection to find a low-dimensional linear mapping that maximizes the Wasserstein distance between projected probability distributions.
result Characterizes the convergence rate of the projected Wasserstein distance and presents practical algorithms.
Improved BP algorithm outperforms loopy BP in MAP inference.
problem Limited understanding and poor performance of belief propagation in graphs with loops.
method Introduced α belief propagation, a minimization of localized α-divergence. result Significantly outperforms loopy BP in fully-connected graphs for MAP inference.
Contagion maps detect network structure in noisy data.
problem Detecting underlying manifold structure in noisy data.
method Using activation times in threshold contagions to map network nodes to high-dimensional space.
result Contagion maps reliably detect manifold structure in noisy data, while Isomap fails.
Study shows monodromy kernels are large, failing to prove commensurability in specific strata.
problem Proving commensurability of mapping class groups through monodromy kernels.
method Analyzing monodromy maps for specific strata in translation surfaces.
result Kernels of monodromy maps contain a non-abelian free group of rank 2.
Test partial effects in Frechet regression on Bures-Wasserstein manifolds.
problem Assessing partial effects in Frechet regression on complex manifolds.
method Sample splitting strategy to estimate covariance matrices and test statistic convergence.
result The test statistic converges to a weighted mixture of chi squared components.
Bayesian HMM for protein alignment state estimation.
problem Estimating the MAP state sequence for a Bayesian HMM.
method Training data with Dirichlet priors, iterative algorithms for MAP path estimation.
result Bayesian setup outperforms frequentist estimation in protein alignment.
We introduce a new discriminant analysis method (Empirical Discriminant Analysis or EDA) for binary classification in machine learning. Given a dataset of feature vectors, this method defines an empirical feature map transforming the training and test data into new data with components having Gaussian empirical distrib…
String kernels are attractive data analysis tools for analyzing string data. Among them, alignment kernels are known for their high prediction accuracies in string classifications when tested in combination with SVM in various applications. However, alignment kernels have a crucial drawback in that they scale poorly du…
A new method learns proper multiclass losses and probabilities.
problem Learning proper multiclass losses for complex classification tasks.
method Extends monotonicity to multiclass problems using convex functions.
result Consistently outperforms natural multiclass baseline on up to 1,000 class datasets.
A new test assesses text similarity between two groups of documents.
problem Comparing similarity between two groups of documents.
method Neural network-based language models estimate entropy, and a test statistic derived from an estimation-and-inference framework is used.
result The proposed test maintains the nominal Type one error rate while offering greater power compared to existing methods.
Machine learning method characterizes network interference in A/B tests.
problem Compromised A/B test reliability due to network interference.
method Causal network motifs and machine learning models.
result Outperforms conventional methods in characterizing network interference.
Path signatures adapted for Lie groups improve action recognition in computer vision.
problem Improving action recognition in computer vision with geometric constraints.
method Lifting path signatures to Lie groups and proving universality and characteristic property.
result Path signatures on Lie groups provide comparable performance to shallow learning approaches in action recognition.
Study uses U-Net for efficient urban planning map semantic segmentation.
problem Manual visual interpretation of urban planning maps is inefficient and time-consuming.
method Utilized U-shape fully convolutional architecture for end-to-end semantic segmentation.
result Achieved high Jaccard similarity coefficient of 93.63% and overall accuracy of 99.36%.