In this paper, we prove that some Gaussian structural equation models with dependent errors having equal variances are identifiable from their corresponding Gaussian distributions. Specifically, we prove identifiability for the Gaussian structural equation models that can be represented as Andersson-Madigan-Perlman cha…
Bayesian method recovers causal structure in SEMs with equal error variances.
problem Recovering causal structure in SEMs with equal error variances.
method Bayesian DAG selection method using g-priors and the key property of minimum expected squared errors.
result The method consistently recovers the true graph without additional distributional assumptions.
Proposes ENVAR for causal discovery in structural VAR models with equal noise variance.
problem Challenges in causal discovery from multivariate time series with contemporaneous effects.
method Introduces observational equivalence and the observational alignment discrepancy for structural VAR models with equal noise variance.
result Shows that multiple structural VAR parameterizations can induce the same stationary observed process law.
The paper analyzes continuous optimization for DAG structure learning and its limitations.
problem The performance of continuous structure learning approaches is not consistent after data standardization.
method Analysis of continuous optimization for DAG structure learning, focusing on equal and non-equal noise variances.
result Continuous structure learning approaches may not perform well after data standardization, especially with non-equal noise variances.
Optimal sample complexity for learning Gaussian DAG models established.
problem Learning the structure of Gaussian DAG models from observational data.
method Established minimax optimal sample complexity for two settings: equal variances without ordering knowledge and general linear models with ordering knowledge.
result Optimal sample complexity n≍qlog(d/q) for both settings, matching undirected graphical models under equal variances. Proposes a modified Morgan-Pitman test for evaluating variances in machine learning models.
problem Limited ability to account for sampling variability in model selection.
method Enhances the classic Morgan-Pitman test for robustness in non-linear models with heavy-tailed distributions or outliers.
result Demonstrates the test's effectiveness and practical utility in model evaluation and selection.
This paper optimizes portfolio selection by penalizing tracking error, improving Sharpe ratio.
problem Optimizing portfolio allocation with a penalty for deviation from a reference portfolio.
method Formulated as a McKean-Vlasov control problem, provides explicit solutions and asymptotic expansions.
result The penalized portfolio strategy outperforms standard mean-variance and reference portfolios in most cases.
Investigates portfolio optimization with and without gearing constraints.
problem Improving portfolio weights for better alignment with expected returns.
method Extends the alpha-weight angle bound to include gearing constraints and uses theoretical arguments and simulations.
result Equally weighted portfolios are not preferable to mean-variance portfolios even with poor forecast ability and a badly conditioned covariance matrix.
We consider structural equation models in which variables can be written as a function of their parents and noise terms, which are assumed to be jointly independent. Corresponding to each structural equation model, there is a directed acyclic graph describing the relationships between the variables. In Gaussian structu…
In this work, we study robust deep learning against abnormal training data from the perspective of example weighting built in empirical loss functions, i.e., gradient magnitude with respect to logits, an angle that is not thoroughly studied so far. Consequently, we have two key findings: (1) Mean Absolute Error (MAE) D…
Maximum Likelihood Estimators (MLE) has many good properties. For example, the asymptotic variance of MLE solution attains equality of the asymptotic Cram{é}r-Rao lower bound (efficiency bound), which is the minimum possible variance for an unbiased estimator. However, obtaining such MLE solution requires calculating t…
Proposes σ-PCA to learn identifiable linear transformations without whitening.
problem Cannot identify axes with equal variances in PCA.
method Unified model for linear and nonlinear PCA, introducing a missing piece to eliminate rotational indeterminacy.
result Eliminates subspace rotational indeterminacy in PCA.
There exist a number of reinforcement learning algorithms which learnby climbing the gradient of expected reward. Their long-runconvergence has been proved, even in partially observableenvironments with non-deterministic actions, and without the need fora system model. However, the variance of the gradient estimator ha…
Deep learning models show bias and variance are aligned, not in trade-off.
problem The classical bias-variance trade-off in deep learning models.
method Empirical evidence and theoretical analysis of bias and variance in deep learning models.
result Squared bias is approximately equal to variance for correctly classified sample points in deep learning models.
VarGrad reduces variance in ELBO gradient estimation for variational inference.
problem Improving the variance of gradient estimators in variational inference.
method VarGrad uses a new log-variance loss to estimate the ELBO gradient, achieving lower variance than the score function method.
result VarGrad offers a lower variance gradient estimator compared to other methods.
In the recent years, banks have sold structured products such as worst-of options, Everest and Himalayas, resulting in a short correlation exposure. They have hence become interested in offsetting part of this exposure, namely buying back correlation. Two ways have been proposed for such a strategy : either pure correl…
Paper introduces dynamic strategies for multi-period investment models.
problem Optimizing investment strategies over multiple periods with risk and return considerations.
method Developed a Bellman principle for discrete time multi-period mean-variance models, leading to dynamic optimal strategies and efficient frontiers.
result Dynamic optimal strategies can achieve higher returns with lower risk compared to the 1/n strategy.
We present a set of log-price integrated variance estimators, equal to the sum of open-high-low-close bridge estimators of spot variances within n subsequent time-step intervals. The main characteristics of some of the introduced estimators is to take into account the information on the occurrence times of the high a…
Integrates prediction models into portfolio optimization for better asset allocation.
problem Traditional portfolio optimization ignores prediction models, leading to suboptimal decisions.
method Developed a framework that combines regression prediction with mean-variance optimization, providing analytical solutions and neural-network-based optimization for inequality constraints.
result Demonstrated through simulations that integrating prediction models improves portfolio performance.
The paper characterizes optimal dynamic portfolios for a modified mean-variance utility.
problem Optimal dynamic portfolio choice for a modified mean-variance utility.
method Complete characterization under minimal assumptions, no restrictions on asset return moments.
result Maximal MMV utility is linked to the monotone Sharpe ratio, with global squared MSR as the nominal yield.
A new statistical concept, lepto-variance, is defined for stock returns using Regression Trees.
problem Understanding the underlying structure of stock returns using statistical methods.
method Defining lepto-variance as the variance that cannot be removed by any regression tree of a specific depth and analyzing stock returns with 1- and 2-bit Regression Trees.
result Lepto-variance quantifies the resolving power of Regression Trees for stock returns, decomposing total variance into lepto-variance and macro-variance.
We prove that the variance swap rate (fair strike) equals the price of a co-terminal European-style contract when the underlying is an exponential Markov process, time-changed by an arbitrary continuous stochastic clock, which has arbitrary correlation with the driving Markov process, provided that the payoff function …
Polynomial-time algorithm learns causal graphs without parametric assumptions.
problem Learning causal graphs from data without assuming linearity or parametric forms.
method Model-free polynomial-time algorithm with finite-sample guarantees.
result Algorithm achieves linear cost in dimension and samples compared to optimal.
Improved heteroscedastic regression using neural networks with provably accurate mean estimates and calibrated variance.
problem Optimizing neural network parameters for heteroscedastic regression leads to suboptimal mean and variance estimates.
method Two simple modifications to optimization to retain accuracy of mean-only models and offer best-in-class variance calibration.
result Mean estimates from the proposed method are provably as accurate as those from a homoscedastic model.
We revisit resampling procedures for error estimation in binary classification in terms of U-statistics. In particular, we exploit the fact that the error rate estimator involving all learning-testing splits is a U-statistic. Thus, it has minimal variance among all unbiased estimators and is asymptotically normally dis…
Using daily returns of the S&P 500 stocks from 2001 to 2011, we perform a backtesting study of the portfolio optimization strategy based on the extreme risk index (ERI). This method uses multivariate extreme value theory to minimize the probability of large portfolio losses. With more than 400 stocks to choose from, ou…
New risk measures improve portfolio diversification and stability.
problem Concentration risk in traditional portfolio optimization methods.
method Equal-correlation portfolio strategy with mathematical optimization.
result Improved risk diversification and stable returns.
Market-based portfolio variance measures risks using trade data.
problem Measuring portfolio risks using traditional methods ignores trade volume randomness.
method Uses time series of trades with securities and portfolio to assess variance.
result Portfolio variance can be decomposed into securities' contributions, accounting for trade volume randomness.
New method improves portfolio allocation using local Gaussian correlation.
problem Asymmetric dependence in asset returns.
method Local Gaussian correlation to extend mean-variance framework.
result New method outperforms existing portfolios for monthly asset returns.
New method corrects Markowitz variance for trading volume fluctuations.
problem Incorrect risk estimates from Markowitz variance in trading environments.
method Modeling portfolio variance based on trade volume fluctuations.
result Market-based variance can significantly differ from Markowitz variance.
The conventional wisdom of mean-variance (MV) portfolio theory asserts that the nature of the relationship between risk and diversification is a decreasing asymptotic function, with the asymptote approximating the level of portfolio systematic risk or undiversifiable risk. This literature assumes that investors hold an…
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…
The paper introduces new portfolio rules beyond mean-variance, addressing asymmetry and uncertainty.
problem Optimizing portfolios with asymmetric returns and uncertainty in expected returns.
method Derives allocation rules for asymmetric Laplace distributed returns and random normal expected returns. Addresses singular covariance matrices and uncertainty in returns.
result Optimal worst-case scenario solution provides a convex alternative to risk parity, improving portfolio stability.
Markowitz' celebrated optimal portfolio theory generally fails to deliver out-of-sample diversification. In this note, we propose a new portfolio construction strategy based on symmetry arguments only, leading to "Eigenrisk Parity" portfolios that achieve equal realized risk on all the principal components of the covar…
New algorithms reduce complexity for solving nonconvex optimization problems with stochastic objectives and constraints.
problem Solving nonconvex optimization problems with stochastic objectives and constraints.
method Single-loop quadratic penalty and augmented Lagrangian algorithms with variance reduction techniques.
result Achieved best-known complexity guarantees for solving nonconvex optimization problems with stochastic objectives and constraints.
FEAT estimates free energy using adaptive transports.
problem Estimating free energy across scientific domains.
method Uses learned transports and stochastic interpolants.
result Provides consistent, minimum-variance estimators.
Though machine learning algorithms excel at minimizing the average loss over a population, this might lead to large discrepancies between the losses across groups within the population. To capture this inequality, we introduce and study a notion we call maximum weighted loss discrepancy (MWLD), the maximum (weighted) d…
This work broadens calibeating to various proper losses using Bregman divergence.
problem Calibration for a wide range of proper losses.
method Regret minimization and Bregman divergence approach.
result U-calibration results for a family of Tsallis losses with logarithmic regret and dimension independence.
A so called Zipf analysis portofolio management technique is introduced in order to comprehend the risk and returns. Two portofoios are built each from a well known financial index. The portofolio management is based on two approaches: one called the "equally weighted portofolio", the other the "confidence parametrized…
This work generalizes calibeating for a broader range of proper losses using Bregman divergence.
problem Calibration for a wide range of proper losses beyond Brier and log loss.
method Regret minimization based on Bregman divergence for a family of proper losses.
result U-calibration results for a family of Tsallis losses with logarithmic regret and dimension independence.
In the market place, diversification reduces risk and provides protection against extreme events by ensuring that one is not overly exposed to individual occurrences. We argue that diversification is best measured by characteristics of the combined portfolio of assets and introduce a measure based on the information en…
Study tight offline learning bounds for linear MDPs using variance information.
problem Understanding statistical limits with linear function representations in offline reinforcement learning.
method Variance-aware pessimistic value iteration (VAPVI) that reweights Bellman residuals based on estimated variances.
result Improved offline learning bounds expressed in terms of system quantities.
VRER selectively reuses samples to improve policy optimization in complex systems.
problem Lack of effective reuse of historical samples in reinforcement learning.
method Variance reduction based experience replay (VRER) framework.
result VRER accelerates policy optimization and enhances performance.
Paper analyzes high-dimensional portfolio risks and finds empirical out-of-sample relative loss is more reliable.
problem Analyzing risks in high-dimensional portfolios using empirical variance.
method Derives asymptotic behavior of out-of-sample variance and relative loss in high-dimensional settings.
result Empirical out-of-sample relative loss is more reliable than variance in high-dimensional portfolios.
Most stochastic optimization methods use gradients once before discarding them. While variance reduction methods have shown that reusing past gradients can be beneficial when there is a finite number of datapoints, they do not easily extend to the online setting. One issue is the staleness due to using past gradients. …
Study introduces a new investment strategy model using lazy factor and probability weights.
problem Optimizing investment strategies in volatile markets with transaction costs.
method Combines Price Portfolio Forecasting and Mean-Variance Models with Transaction Costs, using probability weights as laziness factor coefficients.
result Model demonstrates adaptability and generalizability in transforming investment strategies.
Heuristic algorithm for portfolio optimization reduces solve times to milliseconds.
problem Mean-variance portfolio optimization with various constraints.
method Alternating Direction Method of Multipliers (ADMM).
result Achieves performance bounds and solves problems in milliseconds.
Investigates if adding cryptocurrencies to German portfolios diversifies better, finding mixed results.
problem Improving diversification in German investor portfolios using cryptocurrencies.
method Portfolio analysis with descriptive statistics, graphical methods, and econometric spanning tests, using a customized EWCI.
result Cryptocurrencies can improve diversification in some windows but not as a normal case.