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 data-fitting applications require the solution of an optimization problem involving a sum of large number of functions of high dimensional parameter. Here, we consider the problem of minimizing a sum of n functions over a convex constraint set X⊆Rp where both n and p are lar…
Large scale optimization problems are ubiquitous in machine learning and data analysis and there is a plethora of algorithms for solving such problems. Many of these algorithms employ sub-sampling, as a way to either speed up the computations and/or to implicitly implement a form of statistical regularization. In this …
This paper shows using sub-sample estimates can improve optimization results in large-scale problems.
problem Large-scale optimization problems with uncertain parameters often lead to suboptimal solutions due to mis-specifications or extreme sample characteristics.
method The paper introduces the use of sub-sample estimates to reduce errors in stochastic optimization models, providing theoretical analysis and numerical examples.
result Sub-sample optimization can achieve improved results over full-sample solution estimates in large-scale problems.
We consider the problem of minimizing a sum of n functions over a convex parameter set C⊂Rp where n≫p≫1. In this regime, algorithms which utilize sub-sampling techniques are known to be effective. In this paper, we use sub-sampling techniques together with low-rank approximation …
The standard approach to compressive sampling considers recovering an unknown deterministic signal with certain known structure, and designing the sub-sampling pattern and recovery algorithm based on the known structure. This approach requires looking for a good representation that reveals the signal structure, and sol…
problem Forecasting tail risks in financial markets.
method Developed a Bayesian framework for realized EGARCH models, incorporating multiple realized volatility measures and using robust adaptive Metropolis algorithm for estimation.
result Standardized skewed Student-t distribution and sub-sampled realized range models outperform other models in tail risk forecasting.
For data sets populated by a very well modeled process and by another process of unknown probability density function (PDF), a desired feature when manipulating the fraction of the unknown process (either for enhancing it or suppressing it) consists in avoiding to modify the kinematic distributions of the well modeled …
We propose a randomized second-order method for optimization known as the Newton Sketch: it is based on performing an approximate Newton step using a randomly projected or sub-sampled Hessian. For self-concordant functions, we prove that the algorithm has super-linear convergence with exponentially high probability, wi…
This paper compares and analyzes random projections and column sub-sampling for dimension reduction in regression.
problem Computational efficiency in dimension reduction for large datasets.
method Analysis of random projections and column sub-sampling methods for regression.
result Random projections and column sub-sampling can achieve similar prediction error to Principal Components Regression (PCR) but with less computational cost.
This paper tackles efficient and scalable estimation of a complex model involving stochastic linear combinations of non-linear regressions.
problem Estimating a model involving stochastic linear combinations of non-linear regressions efficiently and scalably.
method The paper provides algorithms for estimating the model under specific assumptions about the variate vector and sample size, using techniques like zero-bias transformation and sub-sampling.
result The paper provides theoretical guarantees for the estimation of the model, showing that the estimation errors are of the order O(np) and O(p1+np) with high probability.
Study examines line search approximations for neural networks using MBSS.
problem Reducing computational cost in training large-scale neural networks.
method Empirical study of quadratic line search approximations for dynamic MBSS loss functions, enforcing different types of function and derivative information.
result Selectively enforcing information in approximations reduces the variance of predicted step sizes.