New semimetrics maximize test power for comparing distributions.
problem Comparing and understanding differences between distributions.
method Features optimized to maximize test power, converging with sample size.
result Linear-time tests achieve comparable performance to state-of-the-art methods.
We provide a unifying framework linking two classes of statistics used in two-sample and independence testing: on the one hand, the energy distances and distance covariances from the statistics literature; on the other, distances between embeddings of distributions to reproducing kernel Hilbert spaces (RKHS), as establ…
We provide a unifying framework linking two classes of statistics used in two-sample and independence testing: on the one hand, the energy distances and distance covariances from the statistics literature; on the other, maximum mean discrepancies (MMD), that is, distances between embeddings of distributions to reproduc…
The paper analyzes SGD with Richardson-Romberg extrapolation for convex optimization problems.
problem Solving strongly convex and smooth minimization problems efficiently.
method Combining SGD with Polyak-Ruppert averaging and Richardson-Romberg extrapolation.
result An expansion of the mean-squared error of the estimator with respect to the number of iterations.
New method recovers clusters in non-convex finite metric spaces with oracle queries.
problem Exact recovery of clusters in non-convex finite metric spaces.
method Introducing (β,γ)-convexity and a deterministic algorithm using oracle queries. result Clusters can be recovered using O(k2logn+k2(6/βγ)dens(X)) same-cluster queries. SGD handles label noise with bounds improving over SGLD.
problem Label noise in non-convex optimization.
method Stochastic gradient descent with uniform dissipativity and smoothness conditions, using Wasserstein distance and algorithmic stability.
result Generalization error bounds with a rate of n−2/3, better than SGLD's n−1/2. MuRiT efficiently computes multi-parameter persistence barcodes.
problem Efficient computation of multi-parameter persistent homology.
method Vietoris-Rips transformation to reduce multi-parameter to single-parameter computation.
result MuRiT computes pathwise persistence barcodes for multi-filtered flag complexes.
Method predicts LFSM increments from past observations using codifference.
problem Forecasting LFSM increments from discrete-time observations.
method Uses codifference for serial dependence, with conditional expectation or projection for α>1 or α<2. result Method shows promising performance in forecasting volatilities, capturing kurtosis and serial dependence.