Related papers: Invariance principle for stochastic processes with…
Second order stationary models in time series analysis are based on the analysis of essential statistics whose computations follow a common pattern. In particular, with a map-reduce nomenclature, most of these operations can be modeled as…
We consider the problem of learning a non-deterministic probabilistic system consistent with a given finite set of positive and negative tree samples. Consistency is defined with respect to strong simulation conformance. We propose learning…
We give a general method of deriving statistical limit theorems, such as the central limit theorem and its functional version, in the setting of ergodic measure preserving transformations. This method is applicable in situations where the…
The principle of maximum entropy is a broadly applicable technique for computing a distribution with the least amount of information possible while constrained to match empirically estimated feature expectations. However, in many real-world…
This paper presents a theory of non-linear integer/real arithmetic and algorithms for reasoning about this theory. The theory can be conceived as an extension of linear integer/real arithmetic with a weakly-axiomatized multiplication…
We revisit random search for stochastic optimization, where only noisy function evaluations are available. We show that the method works under weaker smoothness assumptions than previously considered, and that stronger assumptions enable…
Inspired by recent work on extended image volumes that lays the ground for randomized probing of extremely large seismic wavefield matrices, we present a memory frugal and computationally efficient inversion methodology that uses techniques…
Many applications require stochastic processes specified on two- or higher-dimensional domains; spatial or spatial-temporal modelling, for example. In these applications it is attractive, for conceptual simplicity and computational…
In many interacting particle systems, tagged particles move diffusively upon subtracting a drift. General techniques to prove such `invariance principles' are available for reversible processes (Kipnis-Varadhan) and for non-reversible…
In this paper, we consider a class of slow-fast systems of stochastic partial differential equations where the nonlinearity in the slow equation is not continuous and unbounded. We first provide conditions that ensure the existence of a…
Let $X=\{X_n: n\in\mathbb{N}\}$ be a long memory linear process with innovations in the domain of attraction of an $\alpha$-stable law $(0<\alpha<2)$. Assume that the linear process $X$ has a bounded probability density function $f(x)$.…
It is generally accepted that many time series of practical interest exhibit strong dependence, i.e., long memory. For such series, the sample autocorrelations decay slowly and log-log periodogram plots indicate a straight-line…
In this paper, we develop necessary and sufficient conditions for the validity of a martingale approximation for the partial sums of a stationary process in terms of the maximum of consecutive errors. Such an approximation is useful for…
This paper focuses on generalizing quantiles from the ordering point of view. We propose the concept of partial quantiles, which are based on a given partial order. We establish that partial quantiles are equivariant under order-preserving…
We give an introduction to a notion of weak dependence which is more general than mixing and allows to treat for example processes driven by discrete innovations as they appear with time series bootstrap. As a typical example, we analyze…
The empirical likelihood inference is extended to a class of semiparametric models for stationary, weakly dependent series. A partially linear single-index regression is used for the conditional mean of the series given its past, and the…
Renewal processes are broadly used to model stochastic behavior consisting of isolated events separated by periods of quiescence, whose durations are specified by a given probability law. Here, we identify the minimal sufficient statistic…
High dimensional covariance estimation and graphical models is a contemporary topic in statistics and machine learning having widespread applications. An important line of research in this regard is to shrink the extreme spectrum of the…
Designing models that are both expressive and preserve known invariances of tasks is an increasingly hard problem. Existing solutions tradeoff invariance for computational or memory resources. In this work, we show how to leverage…
A program invariant is a property that holds for every execution of the program. Recent work suggest to infer likely-only invariants, via dynamic analysis. A likely invariant is a property that holds for some executions but is not…