Paper unifies bias and variance models for classification.
problem Different frameworks for bias and variance in classification.
method Unified Tumer & Ghosh and James approaches.
result Closed form relationships between 0/1 loss and squared error loss.
The paper explores generalized quasi-Einstein manifolds and their properties.
problem Investigating properties of generalized quasi-Einstein manifolds under specific conditions.
method Analyzing natural conditions on potential vector fields and deriving consequences.
result The potential vector field is shown to be Killing under suitable integral assumptions.
Paper tackles Byzantine attacks in Federated Learning by clustering and robustifying.
problem Adversarial attacks from Byzantine machines in Federated Learning.
method Iterative Federated Clustering Algorithm (IFCA) with trimmed mean and median aggregation.
result Improved convergence rate for strongly convex loss functions in Byzantine-Robust IFCA.
Uniformly finite Cannon--Thurston fibers in most hyperbolic settings.
problem Existence and finiteness of Cannon--Thurston maps.
method Analysis of proper maps between hyperbolic metric spaces.
result Uniform finiteness of Cannon--Thurston fibers in most known settings.
Maps from rational homology solid tori yield rank inequalities in Heegaard Floer homology.
problem Rank inequalities in Heegaard Floer homology.
method Using Hanselman-Rasmussen-Watson's bordered Floer homology, we extend their proof to rational homology solid tori.
result We provide rank inequalities for Heegaard Floer homology.
In recent times, the use of separable convolutions in deep convolutional neural network architectures has been explored. Several researchers, most notably (Chollet, 2016) and (Ghosh, 2017) have used separable convolutions in their deep architectures and have demonstrated state of the art or close to state of the art pe…
Ricci soliton contact metric manifolds with certain nullity conditions have recently been studied by Ghosh and Sharma. Whereas the gradient case is well-understood, they provided a list of candidates for the nongradient case.These candidates can be realized as Lie groups, but one only knows the structures of the underl…
We present a general method for privacy-preserving Bayesian inference in Poisson factorization, a broad class of models that includes some of the most widely used models in the social sciences. Our method satisfies limited precision local privacy, a generalization of local differential privacy, which we introduce to fo…
We prove an analogue of Sogge's local Lp estimates for Lp norms of restrictions of eigenfunctions to submanifolds, and use it to show that for quantum ergodic eigenfunctions one can get improvements of the results of Burq-Gérard-Tzvetkov, Hu, and Chen-Sogge. The improvements are logarithmic on negatively curved m…
The article defines and compares two types of quantizations on compact manifolds.
problem Quantization on arbitrary compact smooth manifolds.
method Embedding into CP^n and inducing quantizations from there.
result Generalizations of earlier quantization methods.
The paper solves the problem of fitting an ellipsoid to random points efficiently.
problem Finding an ellipsoid that passes through random Gaussian points.
method Constructing a fitting ellipsoid using a decomposition of a random matrix and graph matrix theory.
result The ellipsoid fitting problem transitions from feasible to infeasible at a sharp threshold of n∼d2/4. We prove a quantitative statement of the quantum ergodicity for Hecke--Maass cusp forms on the modular surface. As an application of our result, along a density 1 subsequence of even Hecke--Maass cusp forms, we obtain a sharp lower bound for the L2-norm of the restriction to a fixed compact geodesic segment of $η=…
UDRL fails to converge in stochastic environments with episodic resets.
problem UDRL's convergence in stochastic environments with resets is questioned.
method UDRL is a supervised learning approach that does not use value functions.
result UDRL diverges in a simple stochastic environment with resets.
The paper introduces and characterizes almost ω-Bach solitons on various product manifolds.
problem Characterizing almost ω-Bach solitons on different manifolds.
method Introducing ω-Bach tensor and defining almost ω-Bach solitons; characterizing them under specific conditions. result Explicitly found gradient almost ω-Bach solitons on specific product manifolds.
Gradient EM converges exponentially to optimal solution in agnostic mixtures.
problem Fitting k parametric functions to given data points without a generative model. method Gradient EM algorithm for agnostic mixtures of arbitrary parametric functions.
result Gradient EM converges exponentially to population loss minimizers with high probability.
Improved algorithm for clustered Federated Learning reduces initialization and hyperparameter requirements.
problem Dichotomy between heterogeneous models and simultaneous training in Federated Learning.
method Proposes a new clustering framework and an improved algorithm ( exttt{SR-FCA}) that removes restrictive assumptions.
result Improves clustering accuracy and removes the need for good initialization and hyperparameters.
Polynomial-time algorithm finds planted hypercube vectors in Gaussian mixtures.
problem Clustering d-dimensional Gaussian mixtures with unknown covariance.
method Lattice-based methods using Lenstra--Lenstra--Lovasz reduction.
result Achieves statistically-optimal sample complexity of d+1 samples.
Max-linear regression problem solved with convex programming.
problem Estimating parameters in max-linear regression models.
method Formulated and analyzed a scalable convex program called anchored regression (AR).
result AR provides high probability recovery of parameters with a sample complexity of k4p. Horseshoe priors improve small area estimation by borrowing strength globally but locally.
problem Improving precision of small area estimators through global-local borrowing of strength.
method Developed a tail-robust horseshoe model for Fay-Herriot small area estimation, using heteroscedastic Tweedie identity and regular variation theory.
result The horseshoe model outperforms structured Gaussian smoothing on strongly spatial data, identifying exceptional areas that smoothing suppresses.
We derive a new radial link for binary classification under shared elliptical distributions.
problem Binary classification under shared-generator elliptical class-conditional distributions.
method We derive the Bayes radial-link family from the within-class radius law and estimate it by a finite fractional-power stochastic-polynomial projection.
result The derived link is asymptotically Bayes-optimal and significantly better than QDA on various benchmarks.
New algorithm for decentralized matching markets without prior preference rankings.
problem Decentralized two-sided matching markets without known preference rankings.
method Epoch-based CA-ETC algorithm for decentralized matching markets.
result Achieves player optimal expected regret of O(T_0 (K log T / T_0 Δ^2)^(1/γ) + T_0 (T / T_0)^γ).