This paper optimizes predicting support and resistance levels in financial markets.
problem Optimizing prediction of resistance and support levels in financial markets.
method Assuming a constant elasticity of variance process, the paper derives optimal trading boundaries using the aspiration level hypothesis.
result Optimal trading boundaries serve as predictors of resistance and support levels, located relative to the median interval of the hidden aspiration level.
A new method improves few-shot learning by combining ProtoNet with LFD.
problem Few-shot learning struggles with high variance support sets.
method Combines ProtoNet with Local Fisher Discriminant Analysis.
result Superior classification accuracy on miniImageNet and tieredImageNet.
Meta-learning variance reduced via Laplace approximation for regression tasks.
problem High variance in meta-learning due to limited support data for each task.
method Laplace approximation to estimate posterior variance and reduce gradient estimate variance.
result Effective variance reduction in meta-learning, improving generalization performance.
The bias-variance tradeoff tells us that as model complexity increases, bias falls and variances increases, leading to a U-shaped test error curve. However, recent empirical results with over-parameterized neural networks are marked by a striking absence of the classic U-shaped test error curve: test error keeps decrea…
Given a training set with binary classification, the Support Vector Machine identifies the hyperplane maximizing the margin between the two classes of training data. This general formulation is useful in that it can be applied without regard to variance differences between the classes. Ignoring these differences is not…
Drago optimizes DRO problems with faster convergence.
problem Distributionally robust optimization with closed, convex uncertainty sets.
method Primal-dual coupled variance reduction algorithm with cyclic and randomized updates.
result Achieves state-of-the-art linear convergence rate on strongly convex-strongly concave problems.
VRCQ algorithm reduces variance in Q-learning for MDPs, achieving optimal sample complexity.
problem Estimating the optimal Q-function in MDPs with synchronous sampling.
method VRCQ combines direct variance reduction and Cascade Q-learning.
result VRCQ is minimax optimal and instance optimal for single-action problems.
In this paper, we propose a random projection approach to estimate variance in kernel ridge regression. Our approach leads to a consistent estimator of the true variance, while being computationally more efficient. Our variance estimator is optimal for a large family of kernels, including cubic splines and Gaussian ker…
Importance sampling is often used in machine learning when training and testing data come from different distributions. In this paper we propose a new variant of importance sampling that can reduce the variance of importance sampling-based estimates by orders of magnitude when the supports of the training and testing d…
msPCA solves sparse PCA for multiple components efficiently.
problem Sparse principal component analysis with multiple components.
method Alternating maximization algorithm for sparse loading vectors, with orthogonality or zero correlation constraints.
result Achieves high variance explained with sparse components and controlled feasibility violations.
Recovering the support of sparse vectors in underdetermined linear regression models, \textit{aka}, compressive sensing is important in many signal processing applications. High SNR consistency (HSC), i.e., the ability of a support recovery technique to correctly identify the support with increasing signal to noise rat…
New method reduces variance and bias in approximating indefinite kernels.
problem Approximating non-stationary indefinite kernels with low variance and bias.
method Generalized orthogonal random features (GORF)
result GORF achieves lower variance and approximation error compared to existing methods.
Empirical study finds variance swap rate is affine in spot variance for S&P500 data.
problem Investigating the relationship between variance swap rate and spot variance.
method Empirical analysis using S&P500 data from 2006-2018, testing different models.
result Affine relationship between variance swap rate and spot variance is supported.
Simultaneous orthogonal matching pursuit (SOMP) and block OMP (BOMP) are two widely used techniques for sparse support recovery in multiple measurement vector (MMV) and block sparse (BS) models respectively. For optimal performance, both SOMP and BOMP require \textit{a priori} knowledge of signal sparsity or noise vari…
Paper estimates EOT maps for non-compactly supported measures with subGaussian target.
problem Estimating EOT maps between non-compactly supported measures.
method Uses bias-variance decomposition, T1-transport inequalities, and concentration of measure results.
result Shows error decay rates for different cases of subGaussian measures.
This paper develops scalable control variates for Monte Carlo methods using stochastic optimization.
problem Reducing variance in Monte Carlo estimators for large-scale problems.
method Control variates based on Stein operators, optimized through stochastic optimization.
result Novel theoretical results and empirical validations show effective variance reduction.
Study supports recovery of PDEs from noisy data using a specific regularization method.
problem Support recovery of PDEs from a single noisy trajectory.
method Applying ℓ1-regularized Pseudo-Least Squares model to a given data set.
result Support of ℓ1-c coefficients asymptotically converges to the true signed-support of the PDE.
The lasso has been studied extensively as a tool for estimating the coefficient vector in the high-dimensional linear model; however, considerably less is known about estimating the error variance in this context. In this paper, we propose the natural lasso estimator for the error variance, which maximizes a penalized …
Optimizes variance reduction in Heston model using large and moderate deviations.
problem Improving variance reduction in stochastic volatility models.
method Large and moderate deviations theory applied to Heston model.
result Derives closed-form solutions for optimal change of measure.
Paper proposes CIV estimator for categorical instruments in small sample settings.
problem Estimation with categorical instruments in settings with few observations per category.
method CIV estimator leveraging regularization assumption for latent categorical variable.
result CIV estimator is asymptotically normal, efficient, and semiparametrically efficient under homoskedasticity.
Paper develops methods for statistical inference in SGD with infinite variance.
problem Challenges in statistical inference for SGD with infinite variance.
method Model-agnostic methodology based on weak convergence and subsampling calibration.
result Asymptotically valid confidence regions for SGD in both finite and infinite variance regimes.
We solve a portfolio selection problem with four objectives, finding convex scalarizations for part of the Pareto front.
problem Portfolio selection with four objectives: mean, variance, skewness, and kurtosis.
method Linearly scalarize MVSK objectives into a convex polynomial Fλ over the probability simplex, compute optimizers for each λ. result Identify a set of hyper-parameters for which the scalarization is convex, allowing computation of part of the Pareto front.
In this paper, we consider the optimal portfolio liquidation problem under the dynamic mean-variance criterion and derive time-consistent solutions in three important models. We give adapted optimal strategies under a reconsidered mean-variance subject at any point in time. We get explicit trading strategies in the bas…
The study improves theoretical understanding of using multiple synthetic datasets for better model accuracy.
problem Lack of theoretical understanding of using multiple synthetic datasets for supervised learning.
method Derive bias-variance decompositions for multiple synthetic datasets settings.
result A simple rule of thumb to select the appropriate number of synthetic datasets.
We generalize stochastic smoothing for gradient estimation of non-differentiable functions.
problem Gradient estimation for non-differentiable functions.
method Developed a general framework for relaxation and gradient estimation of non-differentiable black-box functions using stochastic smoothing with reduced assumptions.
result Empirically validated the effectiveness of variance reduction strategies for various non-differentiable tasks.
A large portfolio of independent returns is optimized under the variance risk measure with a ban on short positions. The no-short selling constraint acts as an asymmetric ℓ1 regularizer, setting some of the portfolio weights to zero and keeping the out of sample estimator for the variance bounded, avoiding the di…
Many complex domains, such as robotics control and real-time strategy (RTS) games, require an agent to learn a continuous control. In the former, an agent learns a policy over Rd and in the latter, over a discrete set of actions each of which is parametrized by a continuous parameter. Such problems are natu…
Deep Learning has revolutionized vision via convolutional neural networks (CNNs) and natural language processing via recurrent neural networks (RNNs). However, success stories of Deep Learning with standard feed-forward neural networks (FNNs) are rare. FNNs that perform well are typically shallow and, therefore cannot …
Study shows variance gamma model outperforms Black-Scholes for USD-INR currency options.
problem Complex pricing of currency options with multi-assets.
method Examined USD-INR currency options, tested several models, compared performance.
result Variance gamma model outperforms Black-Scholes model in various volatility regimes.
Study finds AUC is most consistent across different prevalence in binary classification.
problem Consistency of model evaluation metrics across varying prevalence in binary classification.
method Analysis of 156 data scenarios with 18 metrics, 5 models, and a random guess model.
result AUC has the smallest variance in evaluating individual models and ranking of models.
New method reduces density estimation variance for multivariate data.
problem Efficient multivariate density estimation with reduced dimensionality.
method Variance-Reduced Sketching (VRS) framework for multivariate density estimation.
result VRS framework significantly improves density estimation over existing methods.
Many machine learning problems involve Monte Carlo gradient estimators. As a prominent example, we focus on Monte Carlo variational inference (MCVI) in this paper. The performance of MCVI crucially depends on the variance of its stochastic gradients. We propose variance reduction by means of Quasi-Monte Carlo (QMC) sam…
New Stein identity for q-Gaussians reduces gradient variance in machine learning.
problem Improving gradient estimators for non-Gaussian distributions.
method Deriving a new Stein identity for bounded-support q-Gaussians and simplifying previous results.
result Gradient estimators for q-Gaussians have nearly identical forms to Gaussian ones, reducing variance.
We propose an optimization method for minimizing the finite sums of smooth convex functions. Our method incorporates an accelerated gradient descent (AGD) and a stochastic variance reduction gradient (SVRG) in a mini-batch setting. Unlike SVRG, our method can be directly applied to non-strongly and strongly convex prob…
This study analyzes theoretical guarantees for VI with fixed-variance Gaussian mixtures.
problem Theoretical analysis of variational inference with non-Gaussian distributions.
method Formulates variational inference as minimizing a mollified relative entropy, solving it through gradient descent on particle positions.
result Establishes descent lemma and approximation error bounds for optimization of variational inference.
Optimal insurance contract limits insurer's risk exposure variance.
problem Designing an optimal insurance contract limiting insurer's risk exposure variance.
method Derive optimal policy semi-analytically, focusing on actuarially fair case.
result Expected coverage is larger for wealthier insured, indicating normal good.
AdaGrad-Norm achieves optimal convergence rates for non-convex objectives without tuning.
problem Optimal convergence rates for non-convex, smooth objectives with adaptive step sizes.
method Adaptive SGD (AdaGrad-Norm) with self-tuning step sizes, analyzing under unbounded gradients and affine variance scaling.
result AdaGrad-Norm achieves order optimal convergence rate of $\mathcal{O}\left(\frac{\mathrm{poly}\log(T)}{\sqrt{T}}
ight)$ under optimal assumptions.
We develop a conditional sampling scheme for pricing knock-out barrier options under the Linear Transformations (LT) algorithm from Imai and Tan (2006). We compare our new method to an existing conditional Monte Carlo scheme from Glasserman and Staum (2001), and show that a substantial variance reduction is achieved. W…
Investigates how ESG mandates affect portfolio efficiency and risk premia.
problem The inefficiency of portfolios under ESG mandates and the associated risk premia.
method Analyzes equilibrium conditions with ESG constraints and mean-variance investors.
result Negative ESG premium arises due to ESG constraint, not risk factor.
Algorithm identifies best arm in bandit game with variance consideration.
problem Identifying the best arm in a stochastic multi-armed bandit game with varying variances.
method Adaptive algorithm using grouped median elimination to explore gaps and variances.
result Guarantees to output the best arm with probability (1-δ) using optimal number of samples.
The study introduces new liquidity measures and models for assets with extreme liquidity.
problem Modeling assets with extreme liquidity, especially in crypto markets.
method Developed innovative liquidity premium measures, liquidity-adjusted return and volatility models, and used ARMA-GARCH/EGARCH models.
result The liquidity-adjusted models outperform traditional models in predicting asset performance at extreme liquidity.
Improved SVM classification with interpretable features from scattered data.
problem Classification of scattered data points in high-dimensional spaces.
method Truncated ANOVA decomposition for sparse feature selection; use of trigonometric or wavelet feature maps.
result Better classification accuracy and interpretability with ℓ1-norm regularization. High-dimensional predictive models, those with more measurements than observations, require regularization to be well defined, perform well empirically, and possess theoretical guarantees. The amount of regularization, often determined by tuning parameters, is integral to achieving good performance. One can choose the …
We consider the following multi-component sparse PCA problem: given a set of data points, we seek to extract a small number of sparse components with disjoint supports that jointly capture the maximum possible variance. These components can be computed one by one, repeatedly solving the single-component problem and def…
AWNN improves matrix completion by adaptively weighting nearest neighbors.
problem Matrix completion with optimal nearest neighbor weights and radii selection.
method Adaptively weighted nearest neighbor method for matrix completion.
result Theoretical guarantees and synthetic experiments support the effectiveness of AWNN.
W2S FT often outperforms weak teachers due to low intrinsic dimensionality.
problem Understanding why weak-to-strong finetuning outperforms weak models.
method Analyzing W2S in ridgeless regression setting, focusing on variance reduction.
result Weak teacher's variance is inherited by strong student in shared feature subspace, reduced in discrepancy subspace.
Reweighting improves risk bounds in certain data regions.
problem Improving risk bounds in classification and heteroscedastic regression.
method Weighted empirical risk minimization with a data-dependent weight function.
result A weighted ERM estimator can achieve superior performance in specific sub-regions.
DLNs dynamics change with variance, leading to saddle-to-saddle training phases.
problem Understanding the dynamics of DLNs with varying initialization variance.
method Analyzing the phase transition of DLNs' dynamics as variance changes.
result Gradient descent visits a sequence of saddles, reaching a sparse global minimum.