The ratio of two probability densities can be used for solving various machine learning tasks such as covariate shift adaptation (importance sampling), outlier detection (likelihood-ratio test), and feature selection (mutual information). Recently, several methods of directly estimating the density ratio have been deve…
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48 results for “Conditional Least Square”
We study asymptotic properties of some (essentially conditional least squares) parameter estimators for the subcritical Heston model based on discrete time observations derived from conditional least squares estimators of some modified parameters.
Paper proposes a pre-conditioning technique to speed up gradient-descent convergence in distributed linear least-squares problems.
problem Expediting convergence of gradient-descent method for ill-conditioned distributed linear least-squares problems.
method Iterative pre-conditioning technique to improve convergence rate of gradient-descent method.
result Pre-conditioned gradient-descent achieves superlinear convergence for unique solutions and improved linear convergence otherwise.
Efficiently estimates private least squares with linear error growth.
problem Private estimation of ordinary least squares with bounded residuals and leverage.
method Scaled noise added to a stable nonprivate estimator of the regression vector.
result Near-optimal accuracy guarantee with linear error growth in dimension.
Synthesizes robust estimators for domain adaptation.
problem Improving prediction accuracy in target domain with limited data.
method Synthesizes a family of robust least squares estimators using convex optimization.
result Robust strategies can outperform non-robust interpolations.
Consider Least Squares Monte Carlo (LSM) algorithm, which is proposed by Longstaff and Schwartz (2001) for pricing American style securities. This algorithm is based on the projection of the value of continuation onto a certain set of basis functions via the least squares problem. We analyze the stability of the algori…
How many inner simulations to compute conditional expectations with least-square Monte Carlo?math.ST
Optimizes K inner simulations for least-square Monte Carlo to reduce computational cost.
problem Computing conditional expectation E[f (Y)|X] with limited samples.
method Determines optimal number of Y samples (K) for given computational budget.
result Computational gain is maximized when sampling Y given X is inexpensive.
Lower Bounds and a Near-Optimal Shrinkage Estimator for Least Squares using Random Projectionsmath.OC
Improved estimator for least squares using random projections achieves smaller error.
problem Improving the accuracy of least squares solutions for large-scale problems.
method James-Stein estimator applied to Gaussian sketching of least squares problems.
result Upper and lower bounds match when SNR is small and data matrix is well-conditioned.
We prove the statistical consistency of kernel Partial Least Squares Regression applied to a bounded regression learning problem on a reproducing kernel Hilbert space. Partial Least Squares stands out of well-known classical approaches as e.g. Ridge Regression or Principal Components Regression, as it is not defined as…
Improved Least-Squares Monte Carlo with finite-difference ansatz.
problem Improving accuracy and stability in option pricing.
method Constructing an ansatz using finite-difference solution for conditional expected continuation payoffs.
result Reduces mean squared error and final pricing error.
Many problems in financial engineering involve the estimation of unknown conditional expectations across a time interval. Often Least Squares Monte Carlo techniques are used for the estimation. One method that can be combined with Least Squares Monte Carlo is the "Regress-Later" method. Unlike conventional methods wher…
We consider least squares estimation in a general nonparametric regression model. The rate of convergence of the least squares estimator (LSE) for the unknown regression function is well studied when the errors are sub-Gaussian. We find upper bounds on the rates of convergence of the LSE when the errors have uniformly …
CD converges linearly for MCP/SCAD penalized least squares.
problem Recovering sparse signals from data.
method Coordinate descent for MCP/SCAD penalized least squares.
result CD converges linearly to solutions of MCP/SCAD penalized least squares.
Study on hedging risky assets with jumps and costs.
problem Hedging in jump-diffusion models with transaction costs.
method Conditional least square hedging strategy, explicit form for European call options.
result Explicit form of hedging strategy for European call options under transaction costs.
Study of regularized least squares in RKKS with indefinite kernels.
problem Asymptotic properties of regularized least squares with indefinite kernels in RKKS.
method Introducing a bounded hyper-sphere constraint, theoretical demonstration of globally optimal solution, modified error decomposition techniques, matrix perturbation theory.
result Derivation of learning rates in RKKS, same as RKHS under certain conditions.
This paper explores alternative regression techniques in pricing American put options and compares to the least-squares method (LSM) in Monte Carlo implemented by Longstaff-Schwartz, 2001 which uses least squares to estimate the conditional expected payoff to the option holder from continuation. The pricing is done und…
Matrix factorization is a popular approach to solving matrix estimation problems based on partial observations. Existing matrix factorization is based on least squares and aims to yield a low-rank matrix to interpret the conditional sample means given the observations. However, in many real applications with skewed and…
Effective Dimension Adaptive Sketching Methods for Faster Regularized Least-Squares Optimizationcs.LG
New algorithm reduces sketching dimension to effective problem size.
problem Solving L2-regularized least-squares problems efficiently.
method Randomized algorithm using Gaussian and SRHT embeddings.
result Preserves convergence guarantees with reduced embedding dimension.
Study on consistency of ML methods for moving objects in non-stationary environments.
problem Consistency of machine learning methods for moving objects in non-stationary environments.
method Least squares, ridge regression, and -penalized least squares methods under non-stationary spatial-temporal sampling.
result Consistency and asymptotic normality of the estimates under weak conditions.
The -1 norm based optimization is widely used in signal processing, especially in recent compressed sensing theory. This paper studies the solution path of the -1 norm penalized least-square problem, whose constrained form is known as Least Absolute Shrinkage and Selection Operator (LASSO). A solution path …
A fast sketching algorithm solves regularized least squares problems efficiently.
problem Solving large-scale optimization problems with convex or nonconvex regularization.
method Sketching for Regularized Optimization (SRO) algorithm that generates a sketch of the original data matrix and solves the sketched problem.
result General theoretical results for the approximation error between the original and sketched problems, including minimax rates for sparse signal estimation.
Non-Gaussian component analysis (NGCA) is an unsupervised linear dimension reduction method that extracts low-dimensional non-Gaussian "signals" from high-dimensional data contaminated with Gaussian noise. NGCA can be regarded as a generalization of projection pursuit (PP) and independent component analysis (ICA) to mu…
We analyze a simple prefiltered variation of the least squares estimator for the problem of estimation with biased, semi-parametric noise, an error model studied more broadly in causal statistics and active learning. We prove an oracle inequality which demonstrates that this procedure provably mitigates the variance in…
Illustrates interleaved learning with Kalman Filter for linear least squares.
problem Improving machine learning algorithms through interleaved learning.
method Simple statistical and optimization framework based on Kalman Filter.
result Demonstrates the effectiveness of interleaved learning.
Improved SGD for non-strongly-convex regression with faster convergence.
problem Non-strongly-convex least squares regression problems.
method Modified accelerated gradient descent.
result Achieves optimal prediction error rates of and forgets initial conditions faster to .
Conditional expectiles are becoming an increasingly important tool in finance as well as in other areas of applications. We analyse a support vector machine type approach for estimating conditional expectiles and establish learning rates that are minimax optimal modulo a logarithmic factor if Gaussian RBF kernels are u…
Extends phase retrieval methods to handle sensing vector errors.
problem Phase retrieval with errors in sensing vectors.
method Total Least Squares (TLS) framework applied to gradient descent.
result Gradient descent can efficiently solve TLS phase retrieval.
Iterative Hessian sketch: Fast and accurate solution approximation for constrained least-squaresmath.OC
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 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 …
New algorithm reduces rank constrained optimization problems.
problem Rank constrained optimization problems in machine learning and statistics.
method Recursive Importance Sketching (RISRO) algorithm.
result RISRO offers clear advantages over existing algorithms and converges efficiently.
Interacting Particle Systems on Networks: joint inference of the network and the interaction kernelstat.ML
Estimates network structure and interaction rules from multiple agent trajectories.
problem Modeling multi-agent systems on networks from data.
method Jointly infers network topology and interaction kernels using non-convex optimization.
result ORALS estimator is consistent and asymptotically normal under coercivity conditions.
Reinforced optimal controlmath.OC
Improved reinforcement method for optimal control problems.
problem Optimal control problems with limited computational cost.
method Reinforced least squares Monte Carlo method for stochastic control problems.
result Significant improvement in method's efficiency and accuracy.
We consider the Orthogonal Least-Squares (OLS) algorithm for the recovery of a -dimensional -sparse signal from a low number of noisy linear measurements. The Exact Recovery Condition (ERC) in bounded noisy scenario is established for OLS under certain condition on nonzero elements of the signal. The new result a…
No arbitrage SVIq-fin.MF
Characterizes no Butterfly arbitrage in SVI model parameters.
problem No Butterfly arbitrage in SVI implied total variance formula.
method Characterization using intermediary condition from Fukasawa (2012) and rescaling of SVI parameters.
result Simple range conditions on SVI parameters ensure no Butterfly arbitrage.
Investigates least squares estimation in deterministic MoE models.
problem Complexity and difficulty in analyzing MoE models.
method Least squares estimation under deterministic MoE models.
result Rates of estimating strongly identifiable experts are faster than polynomial experts.
The paper improves Kaczmarz algorithm with momentum for linear least squares.
problem Improving convergence of the Kaczmarz algorithm for linear least squares.
method Integrates geometrically smoothed momentum into the randomized Kaczmarz algorithm.
result Proves expected error reduction in singular vector directions.
New algorithm improves online binary classification with constant time complexity.
problem Online binary classification with rebalancing.
method Non-iteratively reweighted recursive least-squares.
result Exacts converges to batch formulation and outperforms existing algorithms.
Optimal weight windows are found by projecting the origin onto a convex polytope.
problem Finding the best weight windows for a weighted moving average smoother.
method Formulated as a quadratic program and projection onto a convex polytope.
result Optimal weight windows are symmetrical and decrease in weight away from the center.
Reduced-rank method improves least-squares regression under output regularity.
problem Least-squares regression with infinite dimensional outputs.
method Reduced-rank method for solving least-squares problems with output regularity assumptions.
result Learning bounds and improved statistical performance compared to full-rank method.
We prove statistical rates of convergence for kernel-based least squares regression from i.i.d. data using a conjugate gradient algorithm, where regularization against overfitting is obtained by early stopping. This method is related to Kernel Partial Least Squares, a regression method that combines supervised dimensio…
Proposes a partitioned least squares model for feature grouping.
problem Modeling with feature groups to assess variable importance.
method Two methods: alternating least squares and exact reformulation.
result Exact method provides better results in less time.
ESNs trained with Tikhonov least squares approximate ergodic dynamical systems in L2(μ) norm.
problem Approximating ergodic dynamical systems using ESNs.
method Tikhonov least squares regression on ESNs trained on observations from an ergodic dynamical system.
result ESNs trained with Tikhonov least squares approximate the target function in the L2(μ) norm.
The kernel least mean squares (KLMS) algorithm is a computationally efficient nonlinear adaptive filtering method that "kernelizes" the celebrated (linear) least mean squares algorithm. We demonstrate that the least mean squares algorithm is closely related to the Kalman filtering, and thus, the KLMS can be interpreted…
A new algorithm solves nonnegative least squares faster with nonnegative data.
problem Nonnegative least squares problems with nonnegative data.
method Primal-dual perspective accelerated algorithm with adaptive restart.
result Oracle complexity independent of matrix constants, solvable to multiplicative error.
Unified methodology for statistical inference in least squares and PCA via randomized sketching.
problem Statistical inference in least squares and PCA problems.
method Randomized sketching and projections, asymptotic normality of quadratic forms.
result Unified statistical inference methods for various sketching distributions.
Optimizes maps with controlled distortion for geometric tasks.
problem Free-boundary diffeomorphism optimization in geometric modeling.
method Least-squares quasiconformal (LSQC) operator and Spectral Beltrami Network (SBN).
result LSQC minimizer well-posed under mild conditions, stable under mesh refinement.
Smooth, globally PŁ functions are essentially nonlinear least-squares.
problem Understanding the structure of functions satisfying the Polyak-Łojasiewicz condition.
method Analyzing smooth functions on Riemannian manifolds with the PŁ condition.
result Smooth, globally PŁ functions are of the form .