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.
We show a principled way of deriving online learning algorithms from a minimax analysis. Various upper bounds on the minimax value, previously thought to be non-constructive, are shown to yield algorithms. This allows us to seamlessly recover known methods and to derive new ones. Our framework also captures such "unort…
Algorithm design is a laborious process and often requires many iterations of ideation and validation. In this paper, we explore automating algorithm design and present a method to learn an optimization algorithm, which we believe to be the first method that can automatically discover a better algorithm. We approach th…
New algorithmic view of ℓ2 regularization using ODEs and path-following methods.
problem Optimizing convex loss functions with ℓ2 regularization.
method Established an equivalence between ℓ2-regularized solution paths and ODEs, proposing path-following algorithms based on homotopy methods and numerical ODE solvers.
result The solution path can be viewed as a hybrid of gradient descent and Newton method, providing novel schemes to choose grid points and reducing computational cost.
One popular method for dealing with large-scale data sets is sampling. For example, by using the empirical statistical leverage scores as an importance sampling distribution, the method of algorithmic leveraging samples and rescales rows/columns of data matrices to reduce the data size before performing computations on…
Crowdsourcing utilizes the wisdom of crowds for collective classification via information (e.g., labels of an item) provided by labelers. Current crowdsourcing algorithms are mainly unsupervised methods that are unaware of the quality of crowdsourced data. In this paper, we propose a supervised collective classificatio…
In this paper, we develop a variant of the well-known Gauss-Newton (GN) method to solve a class of nonconvex optimization problems involving low-rank matrix variables. As opposed to the standard GN method, our algorithm allows one to handle general smooth convex objective function. We show, under mild conditions, that …
Pretraining with expert demonstrations have been found useful in speeding up the training process of deep reinforcement learning algorithms since less online simulation data is required. Some people use supervised learning to speed up the process of feature learning, others pretrain the policies by imitating expert dem…
We examine methods for clustering in high dimensions. In the first part of the paper, we perform an experimental comparison between three batch clustering algorithms: the Expectation-Maximization (EM) algorithm, a winner take all version of the EM algorithm reminiscent of the K-means algorithm, and model-based hierarch…
We develop a mixed least squares Monte Carlo-partial differential equation (LSMC-PDE) method for pricing Bermudan style options on assets whose volatility is stochastic. The algorithm is formulated for an arbitrary number of assets and volatility processes and we prove the algorithm converges almost surely for a class …
This paper characterizes hierarchical clustering methods that abide by two previously introduced axioms -- thus, denominated admissible methods -- and proposes tractable algorithms for their implementation. We leverage the fact that, for asymmetric networks, every admissible method must be contained between reciprocal …
In this article, we advance divide-and-conquer strategies for solving the community detection problem in networks. We propose two algorithms which perform clustering on a number of small subgraphs and finally patches the results into a single clustering. The main advantage of these algorithms is that they bring down si…
In this paper, we provide two new stable online algorithms for the problem of prediction in reinforcement learning, \emph{i.e.}, estimating the value function of a model-free Markov reward process using the linear function approximation architecture and with memory and computation costs scaling quadratically in the siz…
Reweighted l1-algorithms have attracted a lot of attention in the field of applied mathematics. A unified framework of such algorithms has been recently proposed by Zhao and Li. In this paper we construct a few new examples of reweighted l1-methods. These functions are certain concave approximations of the l0-norm func…
Many algorithms for data analysis exist, especially for classification problems. To solve a data analysis problem, a proper algorithm should be chosen, and also its hyperparameters should be selected. In this paper, we present a new method for the simultaneous selection of an algorithm and its hyperparameters. In order…
Clustering is a separation of data into groups of similar objects. Every group called cluster consists of objects that are similar to one another and dissimilar to objects of other groups. In this paper, the K-Means algorithm is implemented by three distance functions and to identify the optimal distance function for c…