JME continually estimates data moments privately and accurately.
problem Private and accurate continual estimation of data moments.
method Uses matrix mechanism and joint sensitivity analysis.
result Improves accuracy in estimating mean and covariance with reduced noise.
PMT uses public data moments to make DP feasible for unbounded data.
problem Applying differential privacy to unbounded data distributions.
method Public-moment-guided Truncation (PMT) using second-moments from public data.
result PMT improves the accuracy and stability of DP models.
Enhances DP linear regression using public data moments.
problem Limited utility of traditional DP methods in linear regression.
method Transform private data using public second-moment matrix for a better OLSE.
result Improved accuracy and robustness of OLSE in DP linear regression.
We consider two stage estimation with a non-parametric first stage and a generalized method of moments second stage, in a simpler setting than (Chernozhukov et al. 2016). We give an alternative proof of the theorem given in (Chernozhukov et al. 2016) that orthogonal second stage moments, sample splitting and n1/4-…
A new memory-efficient Adam variant reduces second moments when feasible.
problem Memory constraints in training machine learning models.
method Signal-to-Noise Ratio (SNR) analysis to identify dimensions where second moments can be replaced by means.
result Memory-efficient Adam variant (SlimAdam) matches performance and stability of Adam while saving up to 98% of second moments.
We extend the classical Cox-Ross-Rubinstein binomial model in two ways. We first develop a binomial model with time-dependent parameters that equate all moments of the pricing tree increments with the corresponding moments of the increments of the limiting Itô price process. Second, we introduce a new trinomial model i…
Dynamic Boltzmann Machine (DyBM) has been shown highly efficient to predict time-series data. Gaussian DyBM is a DyBM that assumes the predicted data is generated by a Gaussian distribution whose first-order moment (mean) dynamically changes over time but its second-order moment (variance) is fixed. However, in many fi…
New optimizer Eve uses examplewise gradients for better second-moment estimates.
problem Improving optimization methods for machine learning.
method Adaptive optimization with examplewise gradients.
result Eve optimizer slightly outperforms Adam on small scale benchmarks.
AdamNX improves Adam's stability by adjusting its learning rate.
problem Adam's tendency to converge to non-flat minima in large-scale models.
method Proposes a novel exponential decay mechanism for Adam's second-order moment estimate.
result AdamNX outperforms Adam and its variants in stability and performance.
New proof of Sobolev inequality with constraints on sphere.
problem Improving Sobolev inequality on sphere with constraints.
method Careful study of extremal problem on sphere.
result Explicit determination of constant in second order moments case.
Paper examines risk measure expansions under FGM dependence, improving accuracy at extreme levels.
problem Capturing higher-order tail behavior and dependence effects in risk measures.
method Second-order asymptotic expansions using extreme value theory and regular variation theory.
result Second-order approximations reduce approximation errors, especially at extreme confidence levels.
New adaptive stepsize method for stochastic approximation converges to target point.
problem Finding optimal step sizes for stochastic approximation algorithms.
method Adaptive block-coordinate stepsizes using online estimates of second moment.
result New method converges almost surely to a small neighborhood of the target point.
In a recent paper [\textit{M. Cristelli, A. Zaccaria and L. Pietronero, Phys. Rev. E 85, 066108 (2012)}], Cristelli \textit{et al.} analysed relation between skewness and kurtosis for complex dynamical systems and identified two power-law regimes of non-Gaussianity, one of which scales with an exponent of 2 and the oth…
Derives moments of PL networks for robust DNNs.
problem Analyzing robustness of DNNs to adversarial attacks.
method Derives exact analytic expressions for moments of PL networks, generalizes variance expression, and constructs sparse and smooth adversarial attacks.
result New variance expressions are tighter and can be efficiently approximated.
Study on eigenvalue distribution of correlated time series, showing deformation of Marchenko-Pastur distribution.
problem Eigenvalue distribution of Wishart matrix with temporal correlation.
method Analysis of moments and convergence to deformed Marchenko-Pastur distribution for Gaussian process with temporal correlation.
result Eigenvalue distribution converges to deformed Marchenko-Pastur distribution with longer tail and higher peak.
For geometries with a closed three-form we briefly overview the notion of multi-moment maps. We then give concrete examples of multi-moment maps for homogeneous hypercomplex and nearly Kaehler manifolds. A special role in the theory is played by Lie algebras with second and third Betti numbers equal to zero. These we c…
In this paper we introduce an efficient fat-tail measurement framework that is based on the conditional second moments. We construct a goodness-of-fit statistic that has a direct interpretation and can be used to assess the impact of fat-tails on central data conditional dispersion. Next, we show how to use this framew…
Study differentially private linear regression with heavy-tailed data.
problem Differentially private ℓ1-norm linear regression with heavy-tailed data. method Exponential mechanism for ℓ2-norm bounded second moment; relaxation to ℓ2-norm bounded θ-th moment; coordinate-wise bounded moments. result Achieved upper bounds for privacy-preserving linear regression under various moment conditions.
This paper examines how data affects risk measures in uncertain distributions.
problem How does distributional ambiguity affect risk measures?
method Formulated and derived simpler dual problems for infinite and finite dimensional robust moment problems.
result Developed theory and conducted experiments in inventory control and portfolio management.
We propose a method of moments (MoM) algorithm for training large-scale implicit generative models. Moment estimation in this setting encounters two problems: it is often difficult to define the millions of moments needed to learn the model parameters, and it is hard to determine which properties are useful when specif…
MOMENT selects and estimates mixed-effects models using moment identities.
problem Selecting and estimating random-effects covariance matrix and fixed-effects coefficients in multiresponse linear mixed-effects models.
method MOMENT is a stage-wise moment-based framework that reduces the random-effects selection problem to a smooth constrained convex optimization problem.
result MOMENT performs competitively and can outperform separate univariate analyses for correlated responses.
We introduce a notion of moment map adapted to actions of Lie groups that preserve a closed three-form. We show existence of our multi-moment maps in many circumstances, including mild topological assumptions on the underlying manifold. Such maps are also shown to exist for all groups whose second and third Lie algebra…
Iteratively reweighted least squares (IRLS) is a widely-used method in machine learning to estimate the parameters in the generalised linear models. In particular, IRLS for L1 minimisation under the linear model provides a closed-form solution in each step, which is a simple multiplication between the inverse of the we…
A new method for uncertainty estimation in neural networks using existing optimization steps.
problem Uncertainty quantification in deep neural networks.
method L2M: Practical posterior Laplace approximation with optimization-driven second moment estimation.
result L2M method yields reasonable results without requiring changes in models or extra computational steps.
In several recently proposed stochastic optimization methods (e.g. RMSProp, Adam, Adadelta), parameter updates are scaled by the inverse square roots of exponential moving averages of squared past gradients. Maintaining these per-parameter second-moment estimators requires memory equal to the number of parameters. For …
New inequality criterion for a mean field equation on spheres.
problem Finding uniqueness in a mean field equation on spheres.
method Established a new Moser-Trudinger-Onofri inequality with a constraint on moments deviation.
result A threshold for deviation is a uniqueness criterion for the mean field equation.
Develops MENT for interpreting and detecting changes in network trajectories.
problem Distortion of network geometry and invalidation of temporal comparisons in dynamic network analysis.
method Develops Multiscale Euclidean Network Trajectories (MENT) framework based on second-moment geometry.
result Validates and interprets network trajectories through isotropic normalization and orthogonal transformations.
Study resolvent convergence for random matrices with general covariance profiles.
problem Analyzing resolvent convergence for random matrices with non-identically distributed columns.
method Using moments of quadratic forms and deterministic equivalents, the study provides bounds on the trace of matrix products.
result The trace of matrix products is close to the trace of a deterministic equivalent, controlled by matrix norms.
Adaptive gradient methods such as Adam have been shown to be very effective for training deep neural networks (DNNs) by tracking the second moment of gradients to compute the individual learning rates. Differently from existing methods, we make use of the most recent first moment of gradients to compute the individual …
Second-order optimization speeds up deep hedging for complex options.
problem Hedging exotic options with market frictions in realistic markets.
method Second-order optimization scheme leveraging pathwise differentiability and Kronecker-factoring.
result Our method optimizes the policy in 1/4 the steps of standard optimization.
Normal distributions ensure asymptotic variance reduction in moment matching Monte Carlo.
problem Asymptotic variance reduction in general integration problems.
method Characterization of conditions for asymptotic variance reduction using normal distributions.
result Asymptotic variance reduction is guaranteed for normal distributions in moment matching Monte Carlo.
We compute the first and second homotopy groups of a class of contact toric manifolds in terms of the images of the associated moment map.
Study compares optimal vs. naive diversification in crypto markets, finds time-varying moments improve performance.
problem Optimizing portfolio construction in volatile crypto markets.
method Examines time-varying moments and transaction costs, incorporates turnover penalty.
result Time-varying moment estimators outperform conventional estimators in practical portfolio construction.
Several new estimation methods have been recently proposed for the linear regression model with observation error in the design. Different assumptions on the data generating process have motivated different estimators and analysis. In particular, the literature considered (1) observation errors in the design uniformly …
Detects adversaries in crowdsourcing to improve accuracy.
problem Adversaries can skew results in crowdsourced classification.
method Analyzes second-order moments of annotator responses to identify and mitigate adversaries.
result The approach can identify and mitigate adversaries in crowdsourcing tasks.
We prove that in metric measure spaces where the entropy functional is K-convex along every Wasserstein geodesic any optimal transport between two absolutely continuous measures with finite second moments lives on a non-branching set of geodesics. As a corollary we obtain that in these spaces there exists only one opti…
The paper examines higher moments in insurance, focusing on coskewness and its impact on actuarial quantities.
problem The impact of higher-order moments on actuarial applications, particularly expected shortfall and life annuity valuation.
method Derives analytical bounds for mixed moments under unspecified dependence structure, applies copula-based mixture model.
result Coskewness and odd-order mixed moments exhibit a monotonic relationship with expected shortfall and annuity premiums.
A new portfolio optimization method using the Sherman-Morrison identity.
problem Portfolio optimization with covariance and variance.
method Sherman-Morrison identity applied to replace covariance with second moment matrix.
result Sherman-Morrison-Markowitz portfolio solves standard portfolio optimization problems.
The study of random walks on hyperbolic spaces and Teichmüller spaces, proving central limit theorems and geodesic tracking.
problem Analyzing random walks on hyperbolic and Teichmüller spaces.
method Proving central limit theorems and geodesic tracking using finite moments and logarithmic moments.
result Translation lengths of random isometries satisfy a central limit theorem if and only if the random walk has finite second moment.
Betas are possibly the most frequently applied tool to analyze how securities relate to the market. While in very widespread use, betas only express dynamics derived from second moment statistics. Financial returns data often deviate from normal assumptions in the sense that they have significant third and fourth order…
Introduces a new price measure and a second-order economic theory for volatility forecasting.
problem Forecasting price volatility in financial markets.
method Develops a new price measure and a second-order economic theory to model price volatility.
result Shows that second-order economic theory improves forecasting of price volatility.
ADOPT optimizes Adam to converge with any β2 without bounded noise.
problem Non-convergence of Adam optimization algorithm.
method ADOPT removes current gradient from second moment estimate and changes momentum update order.
result ADOPT achieves optimal convergence rate of O(1 / √T) with any β2.
In this paper we introduce a new approach to topic modelling that scales to large datasets by using a compact representation of the data and by leveraging the GPU architecture. In this approach, topics are learned directly from the co-occurrence data of the corpus. In particular, we introduce a novel mixture model whic…
Paper proposes an efficient algorithm to handle high-order portfolio moments.
problem Designing portfolios with high-order moments (skewness and kurtosis) is computationally challenging.
method Proposes a SCA algorithm framework for solving high-order portfolios efficiently.
result Demonstrates the efficiency of the proposed algorithm through numerical experiments.
Method estimates posterior model for boundary value problems with uncertain constraints.
problem Estimating posterior probability model for stochastic boundary value problems with uncertain constraints.
method Probabilistic learning inference using Kullback-Leibler divergence and MCMC.
result Method successfully estimates posterior probability measure with constraints.
Study examines robust regression in high dimensions with heavy-tailed data.
problem Analyzing robust regression in high-dimensional settings with heavy-tailed data.
method Sharp asymptotic characterisation of M-estimators and ridge regression in elliptical distributions.
result Ridge regression is optimal and universal for finite second moments but can decay faster without them.
In this paper we extend the results of Kirwan et alii on convexity properties of the moment map for Hamiltonian group actions, and on the connectedness of the fibers of the moment map, to the case of non-compact orbifolds. Our motivation is twofold. First, the category of orbifolds is important in symplectic geometry b…
Independent component analysis (ICA) is the problem of efficiently recovering a matrix A∈Rn×n from i.i.d. observations of X=AS where S∈Rn is a random vector with mutually independent coordinates. This problem has been intensively studied, but all existing efficient algorithms w…