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 study the problem of approximate ranking from observations of pairwise interactions. The goal is to estimate the underlying ranks of n objects from data through interactions of comparison or collaboration. Under a general framework of approximate ranking models, we characterize the exact optimal statistical error …
This paper improves entropy bounds for ranking time-series complexity.
problem Ranking the complexity of time series processes.
method Building on information theoretic bounds, the paper improves the upper bound of conditional differential entropy using Hadamard's inequality and covariance matrix properties.
result The improved bounds can be used to rank the complexity of time series processes.
In this paper, we develop a relative error bound for nuclear norm regularized matrix completion, with the focus on the completion of full-rank matrices. Under the assumption that the top eigenspaces of the target matrix are incoherent, we derive a relative upper bound for recovering the best low-rank approximation of t…
This paper considers the recovery of a low-rank matrix from an observed version that simultaneously contains both (a) erasures: most entries are not observed, and (b) errors: values at a constant fraction of (unknown) locations are arbitrarily corrupted. We provide a new unified performance guarantee on when the natura…
We propose a general framework for reconstructing and denoising single entries of incomplete and noisy entries. We describe: effective algorithms for deciding if and entry can be reconstructed and, if so, for reconstructing and denoising it; and a priori bounds on the error of each entry, individually. In the noiseless…
Matrices of (approximate) low rank are pervasive in data science, appearing in recommender systems, movie preferences, topic models, medical records, and genomics. While there is a vast literature on how to exploit low rank structure in these datasets, there is less attention on explaining why the low rank structure ap…
Sparse coding, which represents a data point as a sparse reconstruction code with regard to a dictionary, has been a popular data representation method. Meanwhile, in database retrieval problems, learning the ranking scores from data points plays an important role. Up to now, these two problems have always been conside…
Consider the task of estimating a 3-order n×n×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…
For the problems of low-rank matrix completion, the efficiency of the widely-used nuclear norm technique may be challenged under many circumstances, especially when certain basis coefficients are fixed, for example, the low-rank correlation matrix completion in various fields such as the financial market and the low-ra…
Study trade-offs between statistical and computational efficiency in variational inference.
problem Optimizing statistical accuracy vs. computational efficiency in Bayesian inference.
method Case study on Gaussian inferential models with diagonal plus low-rank precision matrices, analyzing Bayesian posterior inference and frequentist uncertainty quantification errors.
result Lower-rank models reduce variance and accelerate convergence but increase posterior inference error.
In binary classification and regression problems, it is well understood that Lipschitz continuity and smoothness of the loss function play key roles in governing generalization error bounds for empirical risk minimization algorithms. In this paper, we show how these two properties affect generalization error bounds in …
Unified transformer-based LT-TTD improves ranking efficiency and quality.
problem Decoupled L1 and L2 models in recommendation and search systems cause irreversible error propagation and suboptimal ranking.
method LT-TTD combines two-tower models with transformer expressivity in a unified listwise learning framework, providing theoretical guarantees and UPQE evaluation.
result LT-TTD reduces irretrievable relevant items and achieves better global optimization than disjoint training.
This paper considers the problem of estimating a low-rank matrix from the observation of all or a subset of its entries in the presence of Poisson noise. When we observe all entries, this is a problem of matrix denoising; when we observe only a subset of the entries, this is a problem of matrix completion. In both case…
In this article, we derive a Bayesian model to learning the sparse and low rank PARAFAC decomposition for the observed tensor with missing values via the elastic net, with property to find the true rank and sparse factor matrix which is robust to the noise. We formulate efficient block coordinate descent algorithm and …
A novel regularizer of the PARAFAC decomposition factors capturing the tensor's rank is proposed in this paper, as the key enabler for completion of three-way data arrays with missing entries. Set in a Bayesian framework, the tensor completion method incorporates prior information to enhance its smoothing and predictio…
In this paper, we develop a novel procedure for low-rank tensor regression, namely \emph{\underline{I}mportance \underline{S}ketching \underline{L}ow-rank \underline{E}stimation for \underline{T}ensors} (ISLET). The central idea behind ISLET is \emph{importance sketching}, i.e., carefully designed sketches based on bot…
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 …