arXiv subjects

Alex Kokot

Publications and source records attributed to Alex Kokot.

6 recordsLinked to original sources

arXiv2026

Optimal Design under Interference, Homophily, and Robustness Trade-offs

To minimize the mean squared error (MSE) in global average treatment effect (GATE) estimation under network interference, a popular approach is to use a cluster-randomized design. However, in the presence of homophily, which is common in social networks, cluster randomization can instead increase the MSE. We develop a novel potential outcomes model that accounts for interference, homophily, and heterogeneous variation. In this setting, we establish a framework for optimizing designs for worst-case MSE under the Horvitz-Thompson estimator. This leads to an optimization problem over the covariance matrices of the treatment assignment, trading off interference, homophily, and robustness. We frame and solve this problem using two complementary approaches. The first involves formulating a semidefinite program (SDP) and employing Gaussian rounding, in the spirit of the Goemans-Williamson approximation algorithm for MAXCUT. The second is an adaptation of the Gram-Schmidt Walk, a vector-balancing algorithm which has recently received much attention. Finally, we evaluate the performance of our designs through various experiments on simulated network data and a real village network dataset.

stat.ME↗

arXiv2026

Local EGOP for Continuous Index Learning

We introduce the setting of continuous index learning, in which a function of many variables varies only along a small number of directions at each point. For efficient estimation, it is beneficial for a learning algorithm to adapt, near each point $x$, to the subspace that captures the local variability of the function $f$. We pose this task as kernel adaptation along a manifold with noise, and introduce Local EGOP learning, a recursive algorithm that utilizes the Expected Gradient Outer Product (EGOP) quadratic form as both a metric and inverse-covariance of our target distribution. We prove that Local EGOP learning adapts to the regularity of the function of interest, showing that under a supervised noisy manifold hypothesis, intrinsic dimensional learning rates are achieved for arbitrarily high-dimensional noise. Empirically, we compare our algorithm to the feature learning capabilities of deep learning. Additionally, we demonstrate improved regression quality compared to two-layer neural networks in the continuous single-index setting.

stat.ML↗

arXiv2025

Coreset selection for the Sinkhorn divergence and generic smooth divergences

We introduce CO2, an efficient algorithm to produce convexly-weighted coresets with respect to generic smooth divergences. By employing a functional Taylor expansion, we show a local equivalence between sufficiently regular losses and their second order approximations, reducing the coreset selection problem to maximum mean discrepancy minimization. We apply CO2 to the Sinkhorn divergence, providing a novel sampling procedure that requires poly-logarithmically many data points to match the approximation guarantees of random sampling. To show this, we additionally verify several new regularity properties for entropically regularized optimal transport of independent interest. Our approach leads to a new perspective linking coreset selection and kernel quadrature to classical statistical methods such as moment and score matching. We showcase this method with a practical application of subsampling image data, and highlight key directions to explore for improved algorithmic efficiency and theoretical guarantees.

stat.ML↗

arXiv2022

Euclidean and Affine Curve Reconstruction

We consider practical aspects of reconstructing planar curves with prescribed Euclidean or affine curvatures. These curvatures are invariant under the special Euclidean group and the equi-affine groups, respectively, and play an important role in computer vision and shape analysis. We discuss and implement algorithms for such reconstruction, and give estimates on how close reconstructed curves are relative to the closeness of their curvatures in appropriate metrics. Several illustrative examples are provided.

math.DG↗

arXiv2020

Metrics and Uniqueness Criteria on the Signatures of Closed Curves

This paper explores the paradigm of the differential signature introduced in 1996 by Calabi et al. This methodology has vast implications in fields such as computer vision, where these techniques can potentially be used to verify a person's handwriting is consistent with prior documents, or in medical imaging, to name a few examples. Motivated by examples provided by Hickman in 2011 and Musso and Nicolodi in 2009 regarding key failures in this invariant, we provide new criteria for the correspondence between a curve and its signature to be unique in a general setting. To show this result, we introduce new methods regarding the signature, particularly through the lens of differential equations, and the extension of the signature to include information on higher order derivatives of the curvature function corresponding to the curve and desired group action. We additionally show results regarding the robustness of the signature, showing that under a suitable metric on the space of subsets of $\mathbb{R}^n$, if two signatures are sufficiently close then so too will the corresponding equivalence classes of curves they correspond to, given certain conditions on these signatures.

math.DG↗

arXiv2020

Characteristics of Eigenvalues Realized by Path-Connected Sets of Matrices

We consider path-connected sets of matrices and the induced paths between eigenvalues. We discuss the equivalence relation generated by these paths, and how it relates to the presence of higher multiplicity eigenvalues realized by the set. Particular interest is applied to the convex hull of matrices, where additional characterizations are provided of this phenomena, and computational methods are given for further study.

math-ph↗