Method learns moments for large implicit models, improving image generation quality.
problem Difficulty in defining and selecting moments for training large implicit models.
method Introduced moment network and used asymptotic theory to define and learn better moments.
result MoLM-trained generators outperform other methods in quality and diversity of generated images.
New method tightens sub-Gaussian concentration inequalities.
problem Estimating variance-type parameters of sub-Gaussian distributions.
method Using sub-Gaussian intrinsic moment norm to maximize normalized moments.
result Provides tighter sub-Gaussian concentration inequalities.
A new method for estimating causal parameters from observables reduces the need for finite moment conditions.
problem Estimating causal parameters from observational data with unknown or infinite moment conditions.
method Variational Method of Moments (VMM) for a general class of estimators, including kernel and neural net-based methods.
result VMM estimators are consistent, asymptotically normal, and semiparametrically efficient.
Developed moment estimators for affine stochastic volatility models.
problem Estimating parameters of affine stochastic volatility models.
method Introduced recursive equations for moments and proposed moment estimators.
result Established a central limit theorem and derived asymptotic covariance matrix.
This article investigates parameter estimation of affine term structure models by means of the generalized method of moments. Exact moments of the affine latent process as well as of the yields are obtained by using results derived for p-polynomial processes. Then the generalized method of moments, combined with Quasi-…
Study on martingale property and moment explosions in signature volatility models.
problem Analyzing the martingale property and moment explosions in signature volatility models.
method Fine analysis of the explosion time of a signature stochastic differential equation.
result The price process is a true martingale if and only if the order of the linear form is odd and a correlation parameter is negative.
Study tightens bounds on subsampled differential privacy.
problem Improving differential privacy in subsampled datasets.
method Analytical moments accounting for subsampled RDP mechanisms.
result Tight upper bound on RDP parameters for subsampled mechanisms.
The paper applies Fisher-Rao geometry to beta distributions for moment analysis.
problem Comparing and analyzing moments of probability distributions.
method Derived geodesic equations and sectional curvature on beta distributions' parameter space. Used Fisher-Rao geometry to map canonical moments to beta distributions.
result Uniqueness of Riemannian centroid in beta distributions' parameter space.
This work develops efficient methods for computing moments of Gaussian mixtures.
problem Efficient computation of moments for Gaussian mixtures with large dimensions.
method Theory and numerical methods for implicit computations with moment tensors of Gaussian mixtures.
result Reduced computational and storage costs for moment tensors of Gaussian mixtures.
A new method for smoothing and parameter inference of Markov jump processes.
problem Approximate inference for Markov jump processes with latent variables.
method Moment-based variational inference with partitioning of transition classes.
result Expressed KL divergence in terms of moment functions.
Bayesian framework uses AI-generated data to improve parameter estimation.
problem Parameter estimation in models with unknown or unspecified likelihood.
method Exponentially tilted empirical likelihood with Dirichlet process posterior.
result AI-generated data can provide useful regularization for parameter estimation.
New KCM tests improve specification testing via RKHS.
problem Improving specification tests for econometric models.
method Kernel conditional moment (KCM) tests based on RKHS.
result KCM tests have better finite-sample performance than existing tests.
Improves machine learning consistency with orthogonal moment equations.
problem Improving consistency of machine learning estimates with complex nuisance parameters.
method Employing Neyman-orthogonal moment equations to improve consistency from n−1/4 to n−1/(2k+2). result Second-order orthogonality can improve consistency to n−1/(2k+2). Stochastic Kronecker graphs supply a parsimonious model for large sparse real world graphs. They can specify the distribution of a large random graph using only three or four parameters. Those parameters have however proved difficult to choose in specific applications. This article looks at method of moments estimators…
This paper presents sampling-based speech parameter generation using moment-matching networks for Deep Neural Network (DNN)-based speech synthesis. Although people never produce exactly the same speech even if we try to express the same linguistic and para-linguistic information, typical statistical speech synthesis pr…
Python package ajdmom simplifies moment formula derivation for jump diffusions.
problem Deriving moment formulae for complex jump diffusion processes.
method Automatically generates closed-form expressions and derivatives for any order of moments.
result Enhances usability and usability of affine jump diffusion models.
Mixture modeling is a general technique for making any simple model more expressive through weighted combination. This generality and simplicity in part explains the success of the Expectation Maximization (EM) algorithm, in which updates are easy to derive for a wide class of mixture models. However, the likelihood of…
We present a detailed analysis of \emph{observable} moments based parameter estimators for the Heston SDEs jointly driving the rate of returns Rt and the squared volatilities Vt. Since volatilities are not directly observable, our parameter estimators are constructed from empirical moments of realized volatilitie…
A 1-parameter family of Steiner chains has constant curvature moments.
problem Characterize the curvature moments of a 1-parameter family of Steiner chains.
method Proved constant curvature moments for k=3 using Descartes Circle Theorem; extended to spherical and hyperbolic geometries.
result First k-1 moments of curvatures remain constant in a 1-parameter family of Steiner chains.
Empower efficient representation of distributions through moment-preserving methods.
problem Representing high-dimensional probability measures efficiently and accurately.
method Empower efficient representation of distributions through moment-preserving methods.
result Empowers efficient and accurate representation of high-dimensional probability measures.
Adafactor optimizes neural networks with less memory and similar performance.
problem Memory constraints in adaptive optimization methods.
method Adafactor uses row and column sums of moving averages to estimate per-parameter second moments, reducing memory usage.
result Adafactor achieves similar performance to Adam with minimal auxiliary storage.
Improved spectral methods of moments for robust latent variable model learning.
problem Limited robustness of spectral methods of moments to model misspecification.
method Hierarchical approach using approximate joint diagonalization instead of tensor decomposition.
result Our method outperforms previous tensor decomposition methods in speed and model quality.
Modeling asset trading strategies with noisy information.
problem Understanding heterogeneous trading strategies in markets with information friction.
method Developed a behavioral asset pricing model using a thin set and extended method of moments.
result The model accurately predicts return time series moments of real data.
Estimates high-dimensional posterior densities by marginal distributions and neural networks.
problem High-dimensional probability density estimation for inference is difficult.
method Direct estimation of lower-dimensional marginal distributions, using Moment Networks for fast computation of moments.
result Demonstrates estimation of gravitational wave time series and applications in cosmology.
Empirical comparison of PCA and ICA on noisy time series.
problem Comparing PCA and ICA performance on noisy data.
method Applied PCA and ICA to two simulated noisy time series with varying distribution parameters and noise levels.
result ICA outperforms PCA due to considering higher moments of data distribution.
New method approximates diffusion process posteriors using moment functions.
problem Approximating posteriors of stochastic differential equations.
method Constructs variational process as controlled prior, approximates posterior with moment functions, uses natural gradient descent.
result Richer variational approximations for state-dependent diffusion terms.
Maxout networks study gradients and propose initialization strategies.
problem Complexity in input-output Jacobian distribution complicates stable parameter initialization.
method Obtained bounds on moments of gradients and formulated initialization strategies.
result Parameter initialization strategies improve training of deep maxout networks.
Learning rate needs to decrease with higher data moments for effective ICA in high dimensions.
problem Slower convergence of ICA in high-dimensional data with high-order moments.
method High-dimensional ODE analysis of ICA algorithm under controlled moment structure.
result Critical learning rate threshold for effective ICA when moments are high.
New algorithm learns HMM parameters on Riemannian manifolds.
problem Learning hidden Markov models on non-Euclidean spaces.
method Geometric method of moments algorithm for Riemannian manifolds.
result Significantly improved speed and accuracy compared to existing methods.
Transformer learns to estimate negative binomial parameters efficiently.
problem Parameter estimation for over-dispersed count data in large screens.
method Pre-trained transformer trained on synthetic data generation to invert parameter to count transformation.
result Method of moments provides faster, more efficient, and better-calibrated estimates.
The learning of domain-invariant representations in the context of domain adaptation with neural networks is considered. We propose a new regularization method that minimizes the discrepancy between domain-specific latent feature representations directly in the hidden activation space. Although some standard distributi…
Comparison results for rough and non-rough Heston models, tighter bounds on moment explosion times.
problem Comparing Heston models with and without roughness.
method Comparison principle for non-linear Volterra integral equations.
result Tighter bounds on moment explosion times for rough Heston models.
The paper proposes a method to estimate complex models using machine learning.
problem Estimating the impact of welfare reform on women's welfare participation.
method Regularized orthogonal machine learning for non-linear semiparametric models.
result The proposed Lasso estimator converges at the oracle rate, preserving the single index property.
This work provides a computationally efficient and statistically consistent moment-based estimator for mixtures of spherical Gaussians. Under the condition that component means are in general position, a simple spectral decomposition technique yields consistent parameter estimates from low-order observable moments, wit…
Adaptive t-distribution estimates nonstationary time series using moving moments.
problem Nonstationary time series with varying dependence structure.
method Moving estimator optimizing a weighted log-likelihood, using exponential moving averages for moments.
result Evolution of ν parameter in Student's t-distribution, capturing tail behavior and extreme events.
Paper proposes a new approach for stochastic gradient descent in probabilistic modeling.
problem Finding optimal predictions in probabilistic models with large step sizes.
method Averaging moment parameters instead of natural parameters for constant-step-size stochastic gradient descent.
result Constant-step-size SGD can lead to better predictions in some cases and always converges in infinite-dimensional models.
Estimates RL data for dynamic treatment effects using GMM.
problem Estimating dynamic treatment effects from RL data with nonstationary behavior policies.
method Weighted GMM approach to stabilize variance in adaptive RL settings.
result Valid hypothesis testing and confidence regions for dynamic treatment effects.
Enhances binomial and trinomial models for equity options pricing.
problem Improving accuracy of equity option pricing models.
method Develops time-dependent binomial model and introduces a risk-neutral trinomial tree.
result Equates moments of pricing tree increments to geometric Brownian motion.
SkMM selects data for finetuning by balancing bias and variance.
problem Balancing bias and variance in high-dimensional finetuning.
method Gradient sketching for bias reduction and moment matching for variance reduction.
result Gradient sketching selects samples efficiently and accurately.
We derive expressions for the first three moments of the decision time (DT) distribution produced via first threshold crossings by sample paths of a drift-diffusion equation. The "pure" and "extended" diffusion processes are widely used to model two-alternative forced choice decisions, and, while simple formulae for ac…
Efficient policy learning from observational data using weighted classification reductions.
problem Efficient policy evaluation does not necessarily lead to efficient estimation of policy parameters.
method Proposed an estimation approach based on generalized method of moments, efficient for policy parameters.
result Demonstrated empirical efficiency and regret benefits of a proposed method.
Paper characterizes equilibrium strategies for stochastic control with higher-order moments.
problem Stochastic control problems with higher-order moments.
method Novel characterization of time-consistent control problems, deriving equilibrium conditions via BSDEs.
result Derives sufficient and necessary conditions for an open-loop Nash equilibrium control (ONEC) in a novel way.
The paper derives risk measures for metalog distributions.
problem Deriving risk measures for metalog distributions.
method Closed-form expressions for Conditional Value at Risk and first-order partial moments.
result First-order partial moments are convex with respect to metalog parameters.
DGMM improves Gaussian mixture modeling efficiency and stability.
problem Efficiently estimating Gaussian mixtures in high dimensions.
method Diagonally-weighted generalized method of moments (DGMM).
result DGMM achieves smaller estimation errors with shorter runtime.
DualAdam improves generalization of Adam by integrating its update mechanisms.
problem Adam's tendency to converge to sharp minima leading to suboptimal generalization.
method DualAdam combines Adam and inverse Adam's update mechanisms to enhance generalization.
result DualAdam outperforms Adam and state-of-the-art variants in generalization performance.
The well known maximum-entropy principle due to Jaynes, which states that given mean parameters, the maximum entropy distribution matching them is in an exponential family, has been very popular in machine learning due to its "Occam's razor" interpretation. Unfortunately, calculating the potentials in the maximum-entro…
New estimator learns symmetric dynamics from few observations.
problem Learning parameters of stochastic linear dynamics from limited data.
method Method of moments estimator using T=O(logN) observations. result Achieves small maximum element-wise error on symmetric matrices.
A new UCB algorithm for heavy-tailed bandits with near-optimal regret.
problem Sequential decision making in uncertain environments with heavy-tailed rewards.
method Data-driven, distribution-free UCB algorithm combining resampled median-of-means and UCB.
result Near-optimal regret bound for heavy-tailed distributions.