arXiv research

Model optimal liquidation in asset bubbles with varying entry times.

TATD predicts missing entries in time-evolving tensors by exploiting temporal dependency and sparsity.

Study of a generalized geometric Brownian motion with varying entry and exit rates.

Improved matrix completion for non-uniformly sampled data.

Due to diverse nature of data acquisition and modern applications, many contemporary problems involve high dimensional datum $\x \in \R^\d$ whose entries often lie in a union of subspaces and the goal is to find out which entries of $\x$ match with a particular subspace $\sU$, classically called \emph {matched subspace…

New research shows larger language models improve data processing for diverse entries.

Bi-GAN model for imputing and predicting irregular time-series data.

Study on optimal bubble riding with price-dependent entry times in a mean field game model.

Unified framework infers time-varying graphs from incomplete signals.

Study on market entry timing in stock liquidation with trading constraints.

Paper improves tensor completion by reducing sample entries needed.

New learning methods for open systems with variable agents.

We give an algorithm for completing an order-$m$ symmetric low-rank tensor from its multilinear entries in time roughly proportional to the number of tensor entries. We apply our tensor completion algorithm to the problem of learning mixtures of product distributions over the hypercube, obtaining new algorithmic result…

We present a methodology for probabilistic load forecasting that is based on lasso (least absolute shrinkage and selection operator) estimation. The model considered can be regarded as a bivariate time-varying threshold autoregressive(AR) process for the hourly electric load and temperature. The joint modeling approach…

We propose an algorithm to impute and forecast a time series by transforming the observed time series into a matrix, utilizing matrix estimation to recover missing values and de-noise observed entries, and performing linear regression to make predictions. At the core of our analysis is a representation result, which st…

Researchers have proposed hardware, software, and algorithmic optimizations to improve the computational performance of deep learning. While some of these optimizations perform the same operations faster (e.g., increasing GPU clock speed), many others modify the semantics of the training procedure (e.g., reduced precis…

New algorithms speed up attention computation for large models by limiting matrix entries.

The covariance matrix of a $p$-dimensional random variable is a fundamental quantity in data analysis. Given $n$ i.i.d. observations, it is typically estimated by the sample covariance matrix, at a computational cost of $O(np^{2})$ operations. When $n,p$ are large, this computation may be prohibitively slow. Moreover, …

We consider the matrix completion problem of recovering a structured matrix from noisy and partial measurements. Recent works have proposed tractable estimators with strong statistical guarantees for the case where the underlying matrix is low--rank, and the measurements consist of a subset, either of the exact individ…

This work generalizes transformer attention to capture higher-order correlations efficiently.

Nowadays, organizations collect vast quantities of accounting relevant transactions, referred to as 'journal entries', in 'Enterprise Resource Planning' (ERP) systems. The aggregation of those entries ultimately defines an organization's financial statement. To detect potential misstatements and fraud, international au…

We improve existing results in the field of compressed sensing and matrix completion when sampled data may be grossly corrupted. We introduce three new theorems. 1) In compressed sensing, we show that if the m \times n sensing matrix has independent Gaussian entries, then one can recover a sparse signal x exactly by tr…

Wedge Sampling improves tensor completion with nearly-linear sample complexity.

Congestion prediction represents a major priority for traffic management centres around the world to ensure timely incident response handling. The increasing amounts of generated traffic data have been used to train machine learning predictors for traffic, however this is a challenging task due to inter-dependencies of…

Proposes GLWB-LTC for enhanced life care annuities with dynamic withdrawal strategies and stochastic interest rates.

The completion of low rank matrices from few entries is a task with many practical applications. We consider here two aspects of this problem: detectability, i.e. the ability to estimate the rank $r$ reliably from the fewest possible random entries, and performance in achieving small reconstruction error. We propose a …

We consider the following general hidden hubs model: an $n \times n$ random matrix $A$ with a subset $S$ of $k$ special rows (hubs): entries in rows outside $S$ are generated from the probability distribution $p_0 \sim N(0,σ_0^2)$; for each row in $S$, some $k$ of its entries are generated from $p_1 \sim N(0,σ_1^2)$, $…

We study low rank matrix and tensor completion and propose novel algorithms that employ adaptive sampling schemes to obtain strong performance guarantees. Our algorithms exploit adaptivity to identify entries that are highly informative for learning the column space of the matrix (tensor) and consequently, our results …

We consider the problem of reconstructing a low rank matrix from a subset of its entries and analyze two variants of the so-called Alternating Minimization algorithm, which has been proposed in the past. We establish that when the underlying matrix has rank $r=1$, has positive bounded entries, and the graph $\mathcal{G…

We investigate the sample size requirement for exact recovery of a high order tensor of low rank from a subset of its entries. In the Tucker decomposition framework, we show that the Riemannian optimization algorithm with initial value obtained from a spectral method can reconstruct a tensor of size $n\times n \times\c…

A new method for streaming PCA provides confidence intervals for eigenvector entries.

In this paper, we consider matrix completion from non-uniformly sampled entries including fully observed and partially observed columns. Specifically, we assume that a small number of columns are randomly selected and fully observed, and each remaining column is partially observed with uniform sampling. To recover the …

Optimal timing strategy for mean-reverting price spreads.

Improved 2-bit covariance estimator with reduced operator norm error and no tuning needed.

We give a rigorous analysis of the statistical behavior of gradients in a randomly initialized fully connected network N with ReLU activations. Our results show that the empirical variance of the squares of the entries in the input-output Jacobian of N is exponential in a simple architecture-dependent constant beta, gi…

Principal Components Analysis (PCA) is one of the most widely used dimension reduction techniques. Robust PCA (RPCA) refers to the problem of PCA when the data may be corrupted by outliers. Recent work by Cand{è}s, Wright, Li, and Ma defined RPCA as a problem of decomposing a given data matrix into the sum of a low-ran…

To improve the efficient frontier of the classical mean-variance model in continuous time, we propose a varying terminal time mean-variance model with a constraint on the mean value of the portfolio asset, which moves with the varying terminal time. Using the embedding technique from stochastic optimal control in conti…

Extends tracking guarantees for time-varying variational inequalities.

New method tracks time-varying parameters in data.

In the noisy tensor completion problem we observe $m$ entries (whose location is chosen uniformly at random) from an unknown $n_1 \times n_2 \times n_3$ tensor $T$. We assume that $T$ is entry-wise close to being rank $r$. Our goal is to fill in its missing entries using as few observations as possible. Let $n = \max(n…

Threadneedle is a multi-agent simulation framework, based on a full double entry book keeping implementation of the banking system's fundamental transactions. It is designed to serve as an experimental test bed for economic simulations that can explore the banking system's influence on the macro-economy under varying a…

Matrix factorization (MF) has been widely used to discover the low-rank structure and to predict the missing entries of data matrix. In many real-world learning systems, the data matrix can be very high-dimensional but sparse. This poses an imbalanced learning problem, since the scale of missing entries is usually much…

This paper studies the timing of trades under mean-reverting price dynamics subject to fixed transaction costs. We solve an optimal double stopping problem to determine the optimal times to enter and subsequently exit the market, when prices are driven by an exponential Ornstein-Uhlenbeck process. In addition, we analy…

This paper studies a composite problem involving the decision making of the optimal entry time and dynamic consumption afterwards. In stage-1, the investor has access to full market information subjecting to some information costs and needs to choose an optimal stopping time to initiate stage-2; in stage-2, the investo…

Efficiently completes low-rank matrices with nearly linear time complexity.

New algorithm optimizes positions of CountSketch non-zero entries for better data compression.

Paper uses LLMs to detect financial anomalies.

Consider the task of estimating a 3-order $n \times n \times n$ tensor from noisy observations of randomly chosen entries in the sparse regime. We introduce a similarity based collaborative filtering algorithm for estimating a tensor from sparse observations and argue that it achieves sample complexity that nearly matc…