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.
Least squares kernel based methods have been widely used in regression problems due to the simple implementation and good generalization performance. Among them, least squares support vector regression (LS-SVR) and extreme learning machine (ELM) are popular techniques. However, the noise sensitivity is a major bottlene…
This letter presents an improved version of diffusion least mean ppower (LMP) algorithm for distributed estimation. Instead of sum of mean square errors, a weighted sum of mean square error is defined as the cost function for global and local cost functions of a network of sensors. The weight coefficients are updated b…
The least squares Monte Carlo algorithm has become popular for solving portfolio optimization problems. A simple approach is to approximate the value functions on a discrete grid of portfolio weights, then use control regression to generalize the discrete estimates. However, the classical global control regression can …
We propose a methodology for computing single and multi-asset European option prices, and more generally expectations of scalar functions of (multivariate) random variables. This new approach combines the ability of Monte Carlo simulation to handle high-dimensional problems with the efficiency of function approximation…
The accuracy of least squares calibration using option premiums and particle filtering of price data to find model parameters is determined. Derivative models using exponential Lévy processes are calibrated using regularized weighted least squares with respect to the minimal entropy martingale measure. Sequential impor…
We obtain an improved finite-sample guarantee on the linear convergence of stochastic gradient descent for smooth and strongly convex objectives, improving from a quadratic dependence on the conditioning (L/μ)2 (where L is a bound on the smoothness and μ on the strong convexity) to a linear dependence on L/μ. …
Develops a diagnostic framework for interest rate model calibration, showing equivalence to Weighted Least Squares and revealing boundary-dominated leverage and local parameter instability.
problem Calibration of stochastic interest rate models
method Diagnostic framework using non-linear regression and analytical tractability of At-The-Money caps
result Reveals boundary-dominated leverage and local parameter instability
This work develops robust diffusion recursive least squares algorithms to mitigate the performance degradation often experienced in networks of agents in the presence of impulsive noise. The first algorithm minimizes an exponentially weighted least-squares cost function subject to a time-dependent constraint on the squ…
The paper addresses statistical inference for online decision-making in a contextual bandit setting.
problem Understanding the performance of reward models in online decision-making with contextual information.
method The paper uses the contextual bandit framework with a linear reward model and the ε-greedy policy to address the exploration-exploitation dilemma. It employs the martingale central limit theorem and inverse propensity score weighting to establish asymptotic normality of parameter estimators.
result The online ordinary least squares estimator and the online weighted least squares estimator are asymptotically normal, providing insights into the performance of the reward model.
Presents SPEED, an algorithm for optimal policy evaluation in linear bandits with heteroscedastic noise.
problem Optimal data collection for policy evaluation in linear bandits with heteroscedastic reward noise.
method Formulated an optimal design for weighted least squares estimates, derived the optimal sample allocation, introduced SPEED algorithm, and derived regret bounds.
result SPEED leads to policy evaluation with MSE comparable to oracle strategy and significantly lower than random policy execution.
Dynamic trading strategies, in the spirit of trend-following or mean-reversion, represent an only partly understood but lucrative and pervasive area of modern finance. Assuming Gaussian returns and Gaussian dynamic weights or signals, (e.g., linear filters of past returns, such as simple moving averages, exponential we…
Kernel adaptive filters (KAF) are a class of powerful nonlinear filters developed in Reproducing Kernel Hilbert Space (RKHS). The Gaussian kernel is usually the default kernel in KAF algorithms, but selecting the proper kernel size (bandwidth) is still an open important issue especially for learning with small sample s…
We study randomized sketching methods for approximately solving least-squares problem with a general convex constraint. The quality of a least-squares approximation can be assessed in different ways: either in terms of the value of the quadratic objective function (cost approximation), or in terms of some distance meas…
Cross validation residuals are well known for the ordinary least squares model. Here leave-M-out cross validation is extended to generalised least squares. The relationship between cross validation residuals and Cook's distance is demonstrated, in terms of an approximation to the difference in the generalised residual …
We study the total least squares (TLS) problem that generalizes least squares regression by allowing measurement errors in both dependent and independent variables. TLS is widely used in applied fields including computer vision, system identification and econometrics. The special case when all dependent and independent…
We compare the risk of ridge regression to a simple variant of ordinary least squares, in which one simply projects the data onto a finite dimensional subspace (as specified by a Principal Component Analysis) and then performs an ordinary (un-regularized) least squares regression in this subspace. This note shows that …