Search Results for author:
Found 29 papers, 6 papers with code
Causal Forecasting:Generalization Bounds for Autoregressive Models
Under causal sufficiency, the problem of causal generalization amounts to learning under covariate shifts, albeit with additional structure (restriction to interventional distributions under the VAR model).
Foundations of Comparison-Based Hierarchical Clustering
We address the classical problem of hierarchical clustering, but in a framework where one does not have access to a representation of the objects or their pairwise similarities.
Practical methods for graph two-sample testing
Hypothesis testing for graphs has been an important tool in applied research fields for more than two decades, and still remains a challenging problem as one often needs to draw inference from few replicates of large graphs.
Graphon based Clustering and Testing of Networks: Algorithms and Theory
Using the proposed graph distance, we present two clustering algorithms and show that they achieve state-of-the-art results.
Analysis of Convolutions, Non-linearity and Depth in Graph Neural Networks using Neural Tangent Kernel
The fundamental principle of Graph Neural Networks (GNNs) is to exploit the structural information of the data by aggregating the neighboring nodes using a `graph convolution' in conjunction with a suitable choice for the network architecture, such as depth and activation functions.
A Revenue Function for Comparison-Based Hierarchical Clustering
Comparison-based learning addresses the problem of learning when, instead of explicit features or pairwise similarities, one only has access to comparisons of the form: \emph{Object $A$ is more similar to $B$ than to $C$.}
Two-sample Hypothesis Testing for Inhomogeneous Random Graphs
Given a population of $m$ graphs from each model, we derive minimax separation rates for the problem of testing $P=Q$ against $d(P, Q)>\rho$.
Two-Sample Tests for Large Random Graphs Using Network Statistics
We consider a two-sample hypothesis testing problem, where the distributions are defined on the space of undirected graphs, and one has access to only one observation from each model.
Uniform Hypergraph Partitioning: Provable Tensor Methods and Sampling Techniques
This work is motivated by two issues that arise when a hypergraph partitioning approach is used to tackle computer vision problems: (i) The uniform hypergraphs constructed for higher-order learning contain all edges, but most have negligible weights.
Comparison Based Nearest Neighbor Search
We consider machine learning in a comparison-based setting where we are given a set of points in a metric space, but we have no access to the actual distances between the points.
Consistency of Spectral Hypergraph Partitioning under Planted Partition Model
Hypergraph partitioning lies at the heart of a number of problems in machine learning and network sciences.
Smoothed Functional Algorithms for Stochastic Optimization using q-Gaussian Distributions
This motivates us to study SF schemes for gradient estimation using the q-Gaussian distribution.
Spectral Clustering with Jensen-type kernels and their multi-point extensions
Motivated by multi-distribution divergences, which originate in information theory, we propose a notion of `multi-point' kernels, and study their applications.
Generative Maximum Entropy Learning for Multiclass Classification
In this paper, we introduce a maximum entropy classification method with feature selection for large dimensional data such as text datasets that is generative in nature.
On Power-law Kernels, corresponding Reproducing Kernel Hilbert Space and Applications
Motivated by the importance of power-law distributions in statistical modeling, in this paper, we propose the notion of power-law kernels to investigate power-laws in learning problem.
Consistency of Spectral Partitioning of Uniform Hypergraphs under Planted Partition Model
Spectral graph partitioning methods have received significant attention from both practitioners and theorists in computer science.
On the optimality of kernels for high-dimensional clustering
This is the first work that provides such optimality guarantees for the kernel k-means as well as its convex relaxation.
Near-Optimal Comparison Based Clustering
The goal of clustering is to group similar objects into meaningful partitions.
New Insights into Graph Convolutional Networks using Neural Tangent Kernels
This paper focuses on semi-supervised learning on graphs, and explains the above observations through the lens of Neural Tangent Kernels (NTKs).
Recovery Guarantees for Kernel-based Clustering under Non-parametric Mixture Models
Despite the ubiquity of kernel-based clustering, surprisingly few statistical guarantees exist beyond settings that consider strong structural assumptions on the data generation process.
Learning Theory Can (Sometimes) Explain Generalisation in Graph Neural Networks
While VC Dimension does result in trivial generalisation error bounds in this setting as well, we show that transductive Rademacher complexity can explain the generalisation properties of graph convolutional networks for stochastic block models.
Interpolation and Regularization for Causal Learning
If the confounding strength is negative, causal learning requires weaker regularization than statistical learning, interpolators can be optimal, and the optimal regularization can even be negative.
A Consistent Estimator for Confounding Strength
Regression on observational data can fail to capture a causal relationship in the presence of unobserved confounding.
Improved Representation Learning Through Tensorized Autoencoders
The central question in representation learning is what constitutes a good or meaningful representation.
Wasserstein Projection Pursuit of Non-Gaussian Signals
We consider the general dimensionality reduction problem of locating in a high-dimensional data cloud, a $k$-dimensional non-Gaussian subspace of interesting features.
Fast Adaptive Test-Time Defense with Robust Features
Adaptive test-time defenses are used to improve the robustness of deep neural networks to adversarial examples.
Explaining Kernel Clustering via Decision Trees
Despite the growing popularity of explainable and interpretable machine learning, there is still surprisingly limited work on inherently interpretable clustering methods.
On the Stability of Gradient Descent for Large Learning Rate
There currently is a significant interest in understanding the Edge of Stability (EoS) phenomenon, which has been observed in neural networks training, characterized by a non-monotonic decrease of the loss function over epochs, while the sharpness of the loss (spectral norm of the Hessian) progressively approaches and stabilizes around 2/(learning rate).
When can we Approximate Wide Contrastive Models with Neural Tangent Kernels and Principal Component Analysis?
We provide the first convergence results of NTK for contrastive losses, and present a nuanced picture: NTK of wide networks remains almost constant for cosine similarity based contrastive losses, but not for losses based on dot product similarity.
