HSIC bottleneck trains deep networks without backpropagation.
problem Training deep neural networks with exploding and vanishing gradients.
method HSIC bottleneck, alternative to cross-entropy loss and backpropagation.
result HSIC bottleneck achieves comparable performance to backpropagation.
Recent works investigated the generalization properties in deep neural networks (DNNs) by studying the Information Bottleneck in DNNs. However, the mea- surement of the mutual information (MI) is often inaccurate due to the density estimation. To address this issue, we propose to measure the dependency instead of MI be…
New method speeds up HSIC for multiple variables.
problem Quadratic computational complexity of HSIC for multiple variables.
method Nyström approximation to HSIC for M≥2. result Consistent Nyström HSIC estimator for M≥2. A new kernel test avoids permutations for independence testing.
problem Intractable null distributions of kernel statistics.
method Developed xHSIC and xdCov, avoiding permutations.
result New tests have limiting Gaussian distributions under null.
Counterexamples show HSIC feature selection misses critical features.
problem Feature selection using HSIC misses important features.
method Feature selection via HSIC maximization.
result HSIC feature selection can miss critical features.
New research optimizes HSIC estimation rate for translation-invariant kernels.
problem Optimizing the rate of HSIC estimation for translation-invariant kernels.
method Proved minimax optimal rate of O(n−1/2) for HSIC estimation. result Optimality of various HSIC estimators proven.
Efficiently explains model outputs using HSIC, a dependence measure.
problem Efficiently explain model outputs for various architectures.
method HSIC, RKHS, Reproducing Kernel Hilbert Spaces, black-box attribution.
result Up to 8 times faster than previous methods while maintaining fidelity.
New method tests causal association using noise contrastive backdoor adjustment.
problem Testing causal association in complex settings with many confounders.
method Backdoor-HSIC (bd-HSIC) using HSIC for independence testing.
result Calibrated and powerful for binary and continuous treatments with many confounders.
Maximizes image representation dependence for self-supervised learning.
problem Learning meaningful image representations from unlabeled data.
method Maximizes Hilbert-Schmidt Independence Criterion (HSIC) between image transformations and identity.
result Matches state-of-the-art performance on ImageNet and other vision tasks.
Proposes HSIC-Lasso for selective inference in non-linear data.
problem Detecting influential features in non-linear and high-dimensional data.
method Model-free HSIC-Lasso based on truncated Gaussians and polyhedral lemma.
result Tight control of type-I error even for small sample sizes.
A statistical test of independence may be constructed using the Hilbert-Schmidt Independence Criterion (HSIC) as a test statistic. The HSIC is defined as the distance between the embedding of the joint distribution, and the embedding of the product of the marginals, in a Reproducing Kernel Hilbert Space (RKHS). It has …
Maximum mean discrepancy (MMD), also called energy distance or N-distance in statistics and Hilbert-Schmidt independence criterion (HSIC), specifically distance covariance in statistics, are among the most popular and successful approaches to quantify the difference and independence of random variables, respectively. T…
This paper improves HSIC-based dimensionality reduction for non-linear kernels.
problem Non-convexity of HSIC objective function for non-linear kernels limits optimization efficiency.
method Spectral optimization algorithm with local guarantees and principled initialization.
result Empirical improvements by a factor of 105 in runtime with lower errors. Unified framework for optimal kernel tests across MMD, HSIC, and KSD.
problem Optimal testing in kernel-based hypothesis testing frameworks.
method Unified derivation of minimax rates, adaptive kernel selection methods.
result Unified power results across MMD, HSIC, and KSD.
The article introduces practical estimators for kernel discrepancies.
problem Estimating kernel discrepancies accurately and efficiently.
method Presented various estimators for MMD, HSIC, and KSD, including V-statistics, U-statistics, and incomplete U-statistics. Stressed the importance of kernel bandwidth and introduced adaptive estimators.
result Adaptive estimators combining multiple estimators with various kernels address the problem of kernel selection.
New methods integrate nonlinear, sparse, and multi-view aspects for high-dimensional data analysis.
problem Integrating nonlinear dependence, sparsity, and multi-view data in high-dimensional datasets.
method Proposes HSIC-SGCCA, SA-KGCCA, and TS-KGCCA methods for multi-view high-dimensional data analysis.
result HSIC-SGCCA outperforms competing methods in multi-view variable selection.
We describe a novel non-parametric statistical hypothesis test of relative dependence between a source variable and two candidate target variables. Such a test enables us to determine whether one source variable is significantly more dependent on a first target variable or a second. Dependence is measured via the Hilbe…
This work improves independence tests for high-dimensional data.
problem Detecting subtle dependencies between high-dimensional random variables with complex distributions.
method Develops two approaches to learn powerful independence tests using variational mutual information and HSIC.
result Optimized HSIC tests generally outperform other approaches on detecting structured dependence.
A new non parametric approach to the problem of testing the independence of two random process is developed. The test statistic is the Hilbert Schmidt Independence Criterion (HSIC), which was used previously in testing independence for i.i.d pairs of variables. The asymptotic behaviour of HSIC is established when compu…
Method analyzes hyperparameters using HSIC for better neural network performance.
problem Complex hyperparameter spaces in deep learning.
method Goal-oriented sensitivity analysis using HSIC.
result Robust analysis index quantifies hyperparameters' impact.
HSIC-based method explains GNN structures.
problem Interpreting GNNs' complex dynamics.
method Flexible model-agnostic explanation using HSIC.
result Identifies crucial structures in GNNs.
New statistics improve kernel independence testing efficiency.
problem Improving efficiency in kernel independence testing.
method Adapting martingale MMD construction to joint independence problem.
result Two new statistics achieve finite-sample consistency with linear per-test cost.
Kernel dependence measures yield accurate estimates of nonlinear relations between random variables, and they are also endorsed with solid theoretical properties and convergence rates. Besides, the empirical estimates are easy to compute in closed form just involving linear algebra operations. However, they are hampere…
Paper proposes an algorithm to learn DAGs with indirect dependencies.
problem Learning DAGs misses indirect dependencies in local variables.
method Two-phase algorithm using high-order HSIC for local optimization.
result OT algorithm outperforms existing methods in structure estimation.
New method disentangles hidden data structures using HSIC and supervision.
problem Tackles the challenge of interpreting high-dimensional data.
method Supervised Independent Subspace Principal Component Analysis (sisPCA) using HSIC.
result Identifies and separates hidden data structures effectively.
In this paper, we propose a new kernel-based co-occurrence measure that can be applied to sparse linguistic expressions (e.g., sentences) with a very short learning time, as an alternative to pointwise mutual information (PMI). As well as deriving PMI from mutual information, we derive this new measure from the Hilbert…
This work proves the optimal estimation rates for popular kernel discrepancies.
problem Estimating the disagreement of distributions using kernel discrepancies.
method Proving minimax lower bounds for MMD, HSIC, and KSD.
result The minimax lower bound for estimation of MMD, HSIC, and KSD is \( n^{-1/2} \) on general topological spaces.
Discusses MultiFIT for multivariate dependence, comparing it to HSIC tests.
problem Comparing Multiscale Fisher's Independence Test (MultiFIT) to HSIC tests for multivariate dependence.
method Compares MultiFIT to HSIC tests, highlighting exact level control and performance limitations.
result Observes performance limitations of MultiFIT in terms of test power.
HSIC loss improves robust regression and classification models.
problem Learning robust models in the absence of target domain data.
method Adapted HSIC loss for unsupervised covariate shift.
result Models outperform standard methods on covariate shift tasks.
A crucial challenge in image-based modeling of biomedical data is to identify trends and features that separate normality and pathology. In many cases, the morphology of the imaged object exhibits continuous change as it deviates from normality, and thus a generative model can be trained to model this morphological con…
Proposes a deep network for multi-class classification using spectral training and Gaussian kernel.
problem Multi-class classification with deep networks.
method Spectral training with linear weights and Gaussian kernel activation, constrained on Stiefel Manifold.
result Theoretical guarantee of global optimum and insight into network generalization.
CDSSL improves representation quality by integrating linear and nonlinear dependencies.
problem Scarcity of labeled data and neglect of nonlinear dependencies in SSL.
method CDSSL combines linear correlations and nonlinear dependencies using HSIC in RKHS.
result CDSSL enhances representation quality on diverse benchmarks.
Paper proposes a hybrid loss function for graph self-supervised learning.
problem Improving self-supervised representation learning for graphs.
method Hybrid loss function combining VICReg and HSIC.
result Hybrid loss function outperformed other methods in 4 out of 7 cases.
The paper uses a graph autoencoder to learn unbiased plant-pollinator interaction embeddings.
problem Sampling bias in citizen science data affects ecological network analysis.
method Bipartite graph variational autoencoder with HSIC for fairness.
result The method mitigates sampling bias and provides unbiased embeddings.
Brain imaging data are important in brain sciences yet expensive to obtain, with big volume (i.e., large p) but small sample size (i.e., small n). To tackle this problem, transfer learning is a promising direction that leverages source data to improve performance on related, target data. Most transfer learning methods …
Framework for generating multiple clusterings from multi-view data.
problem Challenges in finding optimal clustering criteria and handling incomplete multi-view data.
method DiMVMC framework that optimizes multiple decoder deep networks to complete data views and generate shared representations.
result DiMVMC outperforms state-of-the-art competitors in generating multiple clusterings with high diversity and quality.
New research shows non-bottlenecked autoencoders can outperform bottlenecked ones for anomaly detection.
problem The necessity of a bottleneck in autoencoders for anomaly detection.
method Investigated two ways to remove bottlenecks: overparameterising the latent layer and introducing skip connections. Carried out extensive experiments on various AE types and datasets.
result Non-bottlenecked autoencoders can outperform bottlenecked ones, improving anomaly detection performance.
Cheap permutation tests speed up distribution testing without sacrificing accuracy.
problem Efficiently testing distribution differences and independence.
method Group datapoints into bins and permute only these bins, using stored sufficient statistics.
result Cheap permutation tests maintain the accuracy and optimality of standard tests but are significantly faster.
SCBMs model causal effects using low-dimensional bottlenecks.
problem Causal effect estimation in high-dimensional systems.
method Structural causal models with low-dimensional summary statistics.
result SCBMs provide a flexible framework for task-specific dimension reduction.
Wide neural networks with narrow bottlenecks behave like deep Gaussian processes.
problem Understanding the behavior of neural networks with narrow layers in the wide limit.
method Analyzing the wide limit of BNNs with narrow bottlenecks, showing they behave like a composition of GPs.
result Wide neural networks with narrow bottlenecks form a composition of GPs, termed a bottleneck NNGP.
Softmax is an output activation function for modeling categorical probability distributions in many applications of deep learning. However, a recent study revealed that softmax can be a bottleneck of representational capacity of neural networks in language modeling (the softmax bottleneck). In this paper, we propose an…
Study shows bottlenecks improve image segmentation quality.
problem Robust object discovery in real-world images remains challenging.
method Empirical investigation of reconstruction bottlenecks in GENESIS model.
result Reconstruction bottlenecks determine reconstruction and segmentation quality.
Deep ResNets favor low bottleneck rank with proper hyperparameters.
problem Understanding the inductive bias of deep neural networks.
method Computed minimum-norm weights of a deep linear ResNet.
result Deep nonlinear ResNets have an inductive bias towards minimizing bottleneck rank.
Derives a new variational approach to information bottleneck.
problem Information theoretic inference and predictive modeling.
method Variational lower bound of predictive information bottleneck.
result Generalizes modern inference procedures and suggests new ones.
Paper revisits Deep Variational Information Bottleneck and proposes a new optimization approach.
problem Limitations of Deep Variational Information Bottleneck in optimizing mutual information.
method Proposes a new optimization approach by circumventing the limitation of requiring both Markov chains during optimisation.
result Shows how to optimise a lower bound for mutual information, circumventing the limitation of requiring both Markov chains.
GraphLIME explains GNN models by selecting key features locally.
problem Explaining the effectiveness of GNN models is challenging due to complex nonlinear transformations.
method GraphLIME uses HSIC Lasso for nonlinear feature selection in GNN models.
result GraphLIME provides more descriptive explanations than existing methods.
CB-APM uses analyst consensus as a bottleneck to interpret stock returns.
problem Tackles the challenge of understanding and predicting stock returns using professional beliefs.
method Embeds analyst consensus as a structural bottleneck, treating it as a sufficient statistic for market information.
result CB-APM portfolios exhibit strong monotonic return gradients and robust across different economic conditions.
Wide neural networks become linear, but adding bottlenecks makes them bilinear or multilinear.
problem Understanding the transition of neural networks from linearity to higher-order functions.
method Analyzing the behavior of randomly initialized wide neural networks with and without bottleneck layers.
result Bottleneck layers transform the network's function from linear to bilinear or multilinear.