A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Many applications generate data with an intrinsic network structure such as time series data, image data or social network data. The network Lasso (nLasso) has been proposed recently as a method for joint clustering and optimization of machine learning models for networked data. The nLasso extends the Lasso from sparse…
This paper presents a novel method to compute the exact Kantorovich-Wasserstein distance between a pair of d-dimensional histograms having n bins each. We prove that this problem is equivalent to an uncapacitated minimum cost flow problem on a (d+1)-partite graph with (d+1)n nodes and dndd+1 arcs,…
Many important optimization problems, such as the minimum spanning tree and minimum-cost flow, can be solved optimally by a greedy method. In this work, we study a learning variant of these problems, where the model of the problem is unknown and has to be learned by interacting repeatedly with the environment in the ba…
In this work, we present a method to compute the Kantorovich-Wasserstein distance of order one between a pair of two-dimensional histograms. Recent works in Computer Vision and Machine Learning have shown the benefits of measuring Wasserstein distances of order one between histograms with n bins, by solving a classic…
We study the question of fair clustering under the {\em disparate impact} doctrine, where each protected class must have approximately equal representation in every cluster. We formulate the fair clustering problem under both the k-center and the k-median objectives, and show that even with two protected classes th…
Embedding representation learning via neural networks is at the core foundation of modern similarity based search. While much effort has been put in developing algorithms for learning binary hamming code representations for search efficiency, this still requires a linear scan of the entire dataset per each query and tr…
The theory of multilayer networks is in its early stages, and its development provides vital methods for understanding complex systems. Multilayer networks, in their multiplex form, have been introduced within the last three years to analysing the structure of financial systems, and existing studies have modelled and e…
Traditionally, practitioners initialize the {\tt k-means} algorithm with centers chosen uniformly at random. Randomized initialization with uneven weights ({\tt k-means++}) has recently been used to improve the performance over this strategy in cost and run-time. We consider the k-means problem with semi-supervised inf…
We consider the minimum cost intervention design problem: Given the essential graph of a causal graph and a cost to intervene on a variable, identify the set of interventions with minimum total cost that can learn any causal graph with the given essential graph. We first show that this problem is NP-hard. We then prove…
In reinforcement learning episodes, the rewards and punishments are often non-deterministic, and there are invariably stochastic elements governing the underlying situation. Such stochastic elements are often numerous and cannot be known in advance, and they have a tendency to obscure the underlying rewards and punishm…
We study the complexity of approximating the multimarginal optimal transport (MOT) distance, a generalization of the classical optimal transport distance, considered here between m discrete probability distributions supported each on n support points. First, we show that the standard linear programming (LP) represe…
MCAL reduces labeling costs by 6x for auto-labeling data sets.
problem Expensive human annotation for ground-truth data sets.
method Iterative approach that trains a classifier to auto-label part of the data set, determining which samples to label using humans and which to label using the classifier at each step.
result 6x lower overall cost compared to human labeling the entire data set, always cheaper than competing strategies.
We study the robustness of active learning (AL) algorithms against prior misspecification: whether an algorithm achieves similar performance using a perturbed prior as compared to using the true prior. In both the average and worst cases of the maximum coverage setting, we prove that all α-approximate algorithms are …
A new procedure for learning cost-sensitive SVM(CS-SVM) classifiers is proposed. The SVM hinge loss is extended to the cost sensitive setting, and the CS-SVM is derived as the minimizer of the associated risk. The extension of the hinge loss draws on recent connections between risk minimization and probability elicitat…
Optimal subset selection for hypothesis testing with penalties.
problem Optimal subset selection of information sources for hypothesis testing with misclassification penalties.
method Proposes a misclassification penalty framework and studies two variants of subset selection problems under centralized Bayesian learning.
result Proves the submodularity of the objective and constraints of the subset selection problems and establishes performance guarantees for greedy algorithms.
Adaptive sequential decision making is one of the central challenges in machine learning and artificial intelligence. In such problems, the goal is to design an interactive policy that plans for an action to take, from a finite set of n actions, given some partial observations. It has been shown that in many applicat…
Streets and Tian introduced pluriclosed flow and symplectic curvature flow in recent years. Here we construct a curvature flow to unify these two flows. We show the short time existence of our flow and exhibit an obstruction to long time existence.
We consider four extended Ricci flow systems---that is, Ricci flow coupled with other geometric flows---and prove dynamical stability of certain classes of stationary solutions of these flows. The systems include Ricci flow coupled with harmonic map flow (studied abstractly and in the context of Ricci flow on warped pr…