New method discovers mean and variance causal graphs from heteroscedastic data.
problem Understanding causal relationships in data with varying variance.
method Bayesian, moment-driven approach inferring separate mean and variance causal graphs.
result Accurately recovers mean and variance structures from heteroscedastic data.
New algorithm detects changes in high-dimensional data with mean and variance.
problem Challenges in detecting changes in high-dimensional data with mean and variance.
method Complete graph-based approach to detect changes of mean and variance from low to high-dimensional online data.
result The proposed method outperforms existing methods in terms of detection power.
The paper develops estimators for variance in graph structures using fused lasso.
problem Variance estimation in graph-structured problems.
method Developed linear time estimator for homoscedastic case and total variation regularization estimator for heteroscedastic case.
result Minimax rates and consistency for variance estimation in various graph structures.
We propose Gaussian processes for signals over graphs (GPG) using the apriori knowledge that the target vectors lie over a graph. We incorporate this information using a graph- Laplacian based regularization which enforces the target vectors to have a specific profile in terms of graph Fourier transform coeffcients, fo…
Study improves understanding of network degree distributions using non-linear ERGs.
problem Lack of models capable of accounting for the variance of empirical degree distributions.
method Defined a fitness-induced variant of the two-star model to reproduce sample variance.
result Non-linear ERGs can reproduce the sample variance of empirical degree distributions.
Paper learns DAGs with quadratic variance functions efficiently.
problem Learning DAGs with quadratic variance functions.
method Introduces topological layers to reconstruct DAGs hierarchically.
result Efficient algorithm reduces computational cost.
Paper explores exact recovery of communities in weighted graphs using Gaussian and exponential distributions.
problem Exact recovery of communities in weighted graphs with Gaussian and exponential distributions.
method Introduces a new semi-metric to describe conditions for exact recovery and analyzes conditions for both complete and incomplete graphs.
result Necessary and sufficient conditions for exact recovery are asymptotically tight and applicable to both complete and incomplete graphs.
A new method for efficient portfolio optimization using graph structures.
problem Optimizing portfolio weights while reducing computational complexity.
method Hierarchical graph structures and Schur complement method.
result Optimal portfolio weights can be computed efficiently by inverting small submatrices.
Learning DAG or Bayesian network models is an important problem in multi-variate causal inference. However, a number of challenges arises in learning large-scale DAG models including model identifiability and computational complexity since the space of directed graphs is huge. In this paper, we address these issues in …
Proposes a new method for big portfolio selection using graph-based conditional moments.
problem Challenges in selecting portfolios for thousands of stocks.
method Graph-based Conditional Moments (GRACE) method: learns quantiles, means, variances, skewness, and kurtosis of stock returns.
result Shows superior performance compared to competitors, especially in measures of conditional variance, skewness, and kurtosis.
Paper solves a control problem with robust methods.
problem Monotone mean-variance problems with stochastic coefficients.
method Finding saddle point through BSDEs with unbounded coefficients.
result Optimal control and value match mean-variance problems.
This paper tackles variance issues in GNN training by proposing a method to reduce both embedding and gradient variances.
problem High variance in estimating stochastic gradients in GNN training, especially in large graphs.
method The paper proposes a decoupled variance reduction strategy that employs approximate gradient information to adaptively sample nodes with minimal variance.
result The proposed method achieves faster convergence and better generalization compared to existing sampling methods.
The paper studies eigenvalues of graph Laplacians on data clouds and proves central limit theorems.
problem Asymptotic fluctuations of eigenvalues of graph Laplacians on data clouds.
method Analysis of graph Laplacian operator, asymptotic fluctuations, central limit theorems.
result Central limit theorems for eigenvalues of graph Laplacians are proven.
While loopy belief propagation (LBP) performs reasonably well for inference in some Gaussian graphical models with cycles, its performance is unsatisfactory for many others. In particular for some models LBP does not converge, and in general when it does converge, the computed variances are incorrect (except for cycle-…
In the continuous time mean-variance model, we want to minimize the variance (risk) of the investment portfolio with a given mean at terminal time. However, the investor can stop the investment plan at any time before the terminal time. To solve this kind of problem, we consider to minimize the variances of the investm…
A new ratio, the Hansen ratio, simplifies mean-variance portfolio theory.
problem Simplifying mean-variance portfolio theory.
method Introducing the Hansen ratio and extending mean-variance theory.
result The Hansen ratio provides a parsimonious description of the mean-variance efficient frontier.
New model recommends stocks considering individual preferences and diversification.
problem Inaccurate stock price predictions and ignoring investment theories.
method Portfolio Temporal Graph Network Recommender (PfoTGNRec) incorporating diversification-enhancing sampling.
result PfoTGNRec outperforms state-of-the-art models in real-world data.
New methods solve graph sparsity optimization problems faster.
problem Complex graph sparsity optimization problems in disease outbreak monitoring and social network analysis.
method Stochastic variance-reduced gradient-based methods GraphSVRG-IHT and GraphSCSG-IHT.
result Our methods achieve linear convergence speed.
A new method uses GATs to optimise portfolios of mid-cap firms, outperforming traditional methods.
problem Optimising portfolios of mid-cap firms considering interdependencies and firms at risk of default.
method Graph Attention Networks (GATs) applied to large-scale financial data.
result The GAT-based portfolio outperforms traditional benchmarks over a long period.
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.
New algorithm for training GNNs with learned weights.
problem Optimal sampling for GNNs with learned weights is intractable.
method Formulated as an adversary bandit problem, optimizing exploration and exploitation.
result Asymptotically approaches optimal variance within a factor of 3.
This note finds closed-form solutions for mean-risk portfolios using a specific type of mixture distribution.
problem Finding optimal portfolios under mean-risk criteria for general distributions.
method Using normal mean-variance mixture (NMVM) distributions, the paper derives closed-form expressions for mean-risk frontiers by optimizing a Markowitz model with adjusted return vectors.
result Closed-form solutions for mean-risk portfolios are found for return vectors following NMVM distributions.
New results on financial equilibria in markets with general semimartingales.
problem Existence and uniqueness of mean-variance equilibria in semimartingale markets.
method Analysis of dynamic mean-variance hedging and fixed-point problems.
result First results allowing for general semimartingales and both discrete and continuous time.
We study the dependence of volatility on the stock price in the stochastic volatility framework on the example of the Heston model. To be more specific, we consider the conditional expectation of variance (square of volatility) under fixed stock price return as a function of the return and time. The behavior of this fu…
New method for portfolio management learns from past wealth evolution.
problem Optimizing portfolio selection based on past performance.
method Simulated annealing clustering for asset selection, considering past wealth evolution.
result Strategy effectively learns from past performance and performs well in practice.
The paper solves MMV and MV problems with random coefficients and finds shared optimal strategies.
problem Optimal trading strategies with random market coefficients.
method Backward stochastic differential equations (BSDEs) to find optimal strategies.
result MMV and MV problems share the same optimal portfolio and value under random coefficients.
Improves Monte-Carlo simulations for consistent mean and variance.
problem Artificial randomness in running mean calculations.
method Combining running mean and variance with accurate summing.
result Increased accuracy and robustness of Monte-Carlo estimates.
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.
This paper addresses the problem of segmenting a time-series with respect to changes in the mean value or in the variance. The first case is when the time data is modeled as a sequence of independent and normal distributed random variables with unknown, possibly changing, mean value but fixed variance. The main assumpt…
The paper analyzes optimal investment strategies for life insurance contracts using mean-variance optimization.
problem Optimal portfolio choice for equity holders in life insurance contracts.
method Mean-variance optimization, explicit formulas, Hamilton-Jacobi-Bellman equations, numerical analysis.
result Equity holders increase investment in risky assets during economic downturns.
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.
Sharp inequalities for matrix means with unknown variance.
problem Estimating matrix means with unknown variance.
method Empirical Bernstein inequalities for symmetric random matrices.
result Adapts to unknown variance with tight deviation bounds.
The paper tackles mean-variance analysis in Bayesian optimization under uncertainty.
problem Optimizing decisions in uncertain environments considering trade-offs between average and variance of risk.
method Developed bounds for mean and variance risk measures in Gaussian Process models and proposed AL algorithms for multi-task, multi-objective, and constrained optimization scenarios.
result Proposed AL algorithms effectively address the mean-variance trade-off in uncertain optimization scenarios.
New framework tests mean-variance spanning in high dimensions.
problem Testing mean-variance spanning in high-dimensional asset spaces.
method Robust Student-t statistic based on batch-mean method, combined using Cauchy combination test.
result Advantages of diversification vary by economic conditions and cross-country.
To improve the efficient frontier of the classical mean-variance model in continuous time, we propose a varying terminal time mean-variance model with a constraint on the mean value of the portfolio asset, which moves with the varying terminal time. Using the embedding technique from stochastic optimal control in conti…
New method solves continuous time mean-variance model for consistent investment strategy.
problem Time-consistent optimal strategy for continuous time mean-variance model.
method Developed a new Bellman principle method.
result Obtained a time-consistent dynamic optimal strategy.
This paper presents a bias-variance tradeoff of graph Laplacian regularizer, which is widely used in graph signal processing and semi-supervised learning tasks. The scaling law of the optimal regularization parameter is specified in terms of the spectral graph properties and a novel signal-to-noise ratio parameter, whi…
In the paper, we consider three quadratic optimization problems which are frequently applied in portfolio theory, i.e, the Markowitz mean-variance problem as well as the problems based on the mean-variance utility function and the quadratic utility.Conditions are derived under which the solutions of these three optimiz…
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 aggregation strategy improves GNN performance and learning dynamics.
problem Improving expressivity and learning dynamics of GNNs.
method Proposes a variance-preserving aggregation function (VPA) for GNNs.
result VPA leads to increased predictive performance and improved learning dynamics.
Algorithm estimates common mean from Gaussian variables with unknown variances.
problem Estimating common mean from Gaussian variables with different unknown variances.
method Intuitive and efficient algorithm using Subset-of-Signals model as benchmark.
result Improved estimation error by polynomial factors compared to previous work.
The multi-armed bandit (MAB) problem is a classical learning task that exemplifies the exploration-exploitation tradeoff. However, standard formulations do not take into account {\em risk}. In online decision making systems, risk is a primary concern. In this regard, the mean-variance risk measure is one of the most co…
NP-PROV separates mean and variance spaces to improve function uncertainty.
problem Neural Processes fail on out-of-domain tasks due to shared latent space uncertainty.
method Separates mean and variance into function-value-related and position-related latent spaces.
result NP-PROV achieves state-of-the-art likelihood with bounded variance in drifts.
Paper optimizes portfolio selection with ICX order constraints.
problem Minimizing portfolio variance with ICX order constraints.
method Optimal and efficient portfolios are derived in closed form.
result Closed-form solutions for optimal and efficient portfolios.
ES-Single uses ES to estimate gradients in unrolled graphs, reducing variance and improving performance.
problem Estimating gradients in unrolled computation graphs with low variance and stability.
method Evolution strategies (ES) applied to unrolled graphs, with a single perturbation per particle.
result ES-Single reduces variance compared to PES, leading to better performance in various tasks.
This paper studies a continuous-time market where an agent, having specified an investment horizon and a targeted terminal mean return, seeks to minimize the variance of the return. The optimal portfolio of such a problem is called mean-variance efficient à la Markowitz. It is shown that, when the market coefficients a…
Regularization helps resolve ambiguity in mean-variance models, improving predictive uncertainty quantification.
problem Signal-to-noise ambiguity in overparameterized mean-variance models.
method Statistical field theory framework to explain phase transition.
result Regularization reduces variability and improves predictive uncertainty quantification.
New estimator accurately estimates mean of real-valued distributions without variance knowledge.
problem Estimating the mean of real-valued distributions without prior variance knowledge.
method Introduces a novel estimator that converges sub-Gaussian and works across distributions with bounded variance.
result The estimator achieves accuracy of σ·(1+o(1))√(2log(1/δ)/n) with parameters n, δ, and σ².