arXiv research

New KCM tests improve specification testing via RKHS.

A new method of moments estimator goes beyond data reweighting.

Kernel methods estimate causal effects with a single proxy for deterministic confounders.

Generative adversarial networks are a novel method for statistical inference that have achieved much empirical success; however, the factors contributing to this success remain ill-understood. In this work, we attempt to analyze generative adversarial learning -- that is, statistical inference as the result of a game b…

We tackle causal inference under conditional moment restrictions using importance weighting.

Deep neural networks improve proximal inference for causal effects.

New method improves estimation of complex models from conditional moment restrictions.

MGD combines maximum entropy and diffusion methods for efficient sampling.

Method learns statistics of return distributions via neural networks and maximum mean discrepancy.

Generalizes moment-matching for exponential families with conditioning or hidden data.

Suppose that we are given a time series where consecutive samples are believed to come from a probabilistic source, that the source changes from time to time and that the total number of sources is fixed. Our objective is to estimate the distributions of the sources. A standard approach to this problem is to model the …

A new filter reduces density fitting to a linear solve, improving performance on nonlinear systems.

Researchers use Gaussian processes to approximate Lagrange multipliers for Maximum-Entropy distributions.

We introduce a simple method for nearly simultaneous computation of all moments needed for quasi maximum likelihood estimation of parameters in discretely observed stochastic differential equations commonly seen in finance. The method proposed in this papers is not restricted to any particular dynamics of the different…

Many inference problems involving questions of optimality ask for the maximum or the minimum of a finite set of unknown quantities. This technical report derives the first two posterior moments of the maximum of two correlated Gaussian variables and the first two posterior moments of the two generating variables (corre…

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 SGMM algorithm for efficient estimation of moment restriction models.

Enhances flexibility in data reweighting with optimal transport and maximum entropy principles.

The paper classifies ruled surfaces in Lorentz-Minkowski space that are stationary for the moment of inertia.

We provide an approach for learning deep neural net representations of models described via conditional moment restrictions. Conditional moment restrictions are widely used, as they are the language by which social scientists describe the assumptions they make to enable causal inference. We formulate the problem of est…

Given a finite set of unknown distributions or arms that can be sampled, we consider the problem of identifying the one with the maximum mean using a $δ$-correct algorithm (an adaptive, sequential algorithm that restricts the probability of error to a specified $δ$) that has minimum sample complexity. Lower bounds for …

We show that the moment explosion time in the rough Heston model [El Euch, Rosenbaum 2016, arxiv:1609.02108] is finite if and only if it is finite for the classical Heston model. Upper and lower bounds for the explosion time are established, as well as an algorithm to compute the explosion time (under some restrictions…

Paper develops methods for inference on time series data using neural networks and sieves.

A new algorithm uses IVs to learn optimal policies from observational data.

Paper tackles stochastic control with mean and higher-order moments, finding Nash equilibria.

Novel framework synthesizes stochastic trajectories with anticipated structural breaks.

Transformer learns to estimate negative binomial parameters efficiently.

In this paper we shall illustrate that each polytopal moment-angle complex can be understood as the intersection of the minima of corresponding Siegel leaves and the unit sphere, with respect to the maximum norm. Consequently, an alternative proof of a rigidity theorem of Bosio and Meersseman is obtained; as piecewise …

The ability of many powerful machine learning algorithms to deal with large data sets without compromise is often hampered by computationally expensive linear algebra tasks, of which calculating the log determinant is a canonical example. In this paper we demonstrate the optimality of Maximum Entropy methods in approxi…

Parameter estimation in Markov random fields (MRFs) is a difficult task, in which inference over the network is run in the inner loop of a gradient descent procedure. Replacing exact inference with approximate methods such as loopy belief propagation (LBP) can suffer from poor convergence. In this paper, we provide a d…

Econophysics, is based on the premise that some ideas and methods from physics can be applied to economic situations. We intend to show in this paper how a physics concept such as entropy can be applied to an economic problem. In so doing, we demonstrate how information in the form of observable data and moment constra…

Paper proposes a policy gradient method for confounded POMDPs.

We construct open book structures on all moment-angle manifolds and describe the topology of their leaves and bindings under certain restrictions. II. We also show, using a recent deep result about contact forms due to Borman, Eliashberg and Murphy [6], that every odd-dimensional moment-angle manifold admits a contact …

A scalable method for estimating spatial data using VREML.

The sequence of moments of a vector-valued random variable can characterize its law. We study the analogous problem for path-valued random variables, that is stochastic processes, by using so-called robust signature moments. This allows us to derive a metric of maximum mean discrepancy type for laws of stochastic proce…

Moment-angle manifolds provide a wide class of examples of non-Kaehler compact complex manifolds. A complex moment-angle manifold Z is constructed via certain combinatorial data, called a complete simplicial fan. In the case of rational fans, the manifold Z is the total space of a holomorphic bundle over a toric variet…

We study concentration phenomena of eigenfunctions of the Laplacian on closed Riemannian manifolds. We prove that the volume measure of a closed manifold concentrates around nodal sets of eigenfunctions exponentially. Applying the method of Colding and Minicozzi we also prove restricted exponential concentration inequa…

The problem of determining the joint probability distributions for correlated random variables with pre-specified marginals is considered. When the joint distribution satisfying all the required conditions is not unique, the "most unbiased" choice corresponds to the distribution of maximum entropy. The calculation of t…

Consider the Slepian process $S$ defined by $S(t)=B(t+1)-B(t),t\in [0,1]$ with $B(t),t\in \R$ a standard Brownian motion.In this contribution we analyze the joint distribution between the maximum $m_{s}=\max_{0\leq u\leq s}S(u)$ certain and the maximum $M_t=\max_{0\leq u\leq t}S(u)$ for $0< s < t$ fixed. Explicit inte…

Learning rate needs to decrease with higher data moments for effective ICA in high dimensions.

New maximum score estimators using ReLU functions and deep neural networks.

DML-CMR estimator reduces bias in CMR problems using deep neural networks.

It is shown that a small cover (resp. real moment-angle manifold) over a simple polytope is an infra-solvmanifold if and only if it is diffeomorphic to a real Bott manifold (resp. flat torus). Moreover, we obtain several equivalent conditions for a small cover being homeomorphic to a real Bott manifold. In addition, we…

New method estimates latent gene expression factors without overlap with known confounders.

Optimizes graph spectral density learning for large networks.

A method learns representations for conditional moment models with controlled ill-posedness.

The paper strengthens the classical result of MLE convergence to a Gaussian distribution.

Efficient approximation lies at the heart of large-scale machine learning problems. In this paper, we propose a novel, robust maximum entropy algorithm, which is capable of dealing with hundreds of moments and allows for computationally efficient approximations. We showcase the usefulness of the proposed method, its eq…