Related papers: Approximate Likelihood Construction for Rough Diff…
We generalize the optimal coupling theorem to multiple random variables: Given a collection of random variables, it is possible to couple all of them so that any two differ with probability comparable to the total-variation distance between…
Likelihood based-learning of graphical models faces challenges of computational-complexity and robustness to model mis-specification. This paper studies methods that fit parameters directly to maximize a measure of the accuracy of predicted…
Randomized higher-order computation can be seen as being captured by a lambda calculus endowed with a single algebraic operation, namely a construct for binary probabilistic choice. What matters about such computations is the probability of…
Recent work on Path-Dependent Partial Differential Equations (PPDEs) has shown that PPDE solutions can be approximated by a probabilistic representation, implemented in the literature by the estimation of conditional expectations using…
Characterizing the risk of operations is a fundamental requirement in robotics, and a crucial ingredient of safe planning. The problem is multifaceted, with multiple definitions arising in the vast recent literature fitting different…
In this paper, an alternative Discrete skew Logistic distribution is proposed, which is derived by using the general approach of discretizing a continuous distribution while retaining its survival function. The properties of the…
Our work introduces an approach for estimating the contribution of attachment mechanisms to the formation of growing networks. We present a generic model in which growth is driven by the continuous attachment of new nodes according to…
Finite-precision floating point arithmetic unavoidably introduces rounding errors which are traditionally bounded using a worst-case analysis. However, worst-case analysis might be overly conservative because worst-case errors can be…
Estimation of finite mixture models when the mixing distribution support is unknown is an important problem. This paper gives a new approach based on a marginal likelihood for the unknown support. Motivated by a Bayesian Dirichlet prior…
We study rare events in systems of diffusive fields driven out of equilibrium by the boundaries. We present a numerical technique and use it to calculate the probabilities of rare events in one and two dimensions. Using this technique, we…
In this paper, we investigate a deep learning method for predicting path-dependent processes based on discretely observed historical information. This method is implemented by considering the prediction as a nonparametric regression and…
In this paper, a modification of the conventional approximations to the quasi-maximum likelihood method is introduced for the parameter estimation of diffusion processes from discrete observations. This is based on a convergent…
This paper presents a detailed theoretical analysis of the three stochastic approximation proximal gradient algorithms proposed in our companion paper [49] to set regularization parameters by marginal maximum likelihood estimation. We prove…
We consider multi-dimensional Gaussian processes and give a new condition on the covariance, simple and sharp, for the existence of stochastic area(s). Gaussian rough paths are constructed with a variety of weak and strong approximation…
In the following article we consider approximate Bayesian computation (ABC) for certain classes of time series models. In particular, we focus upon scenarios where the likelihoods of the observations and parameter are intractable, by which…
We consider a random variable $Y$ and approximations $Y\_n$, defined on the same probability space with values in the same measurable space as $Y$. We are interested in situations where the approximations $Y\_n$ allow to define a Dirichlet…
Master equations are common descriptions of mesoscopic systems. Analytical solutions to these equations can rarely be obtained. We here derive an analytical approximation of the time-dependent probability distribution of the master equation…
We study controlled differential equations driven by a rough path (in the sense of T. Lyons) with an additional, possibly unbounded drift term. We show that the equation induces a solution flow if the drift grows at most linearly.…
We investigate approximating joint distributions of random processes with causal dependence tree distributions. Such distributions are particularly useful in providing parsimonious representation when there exists causal dynamics among…
We study one-dimensional nearest neighbour random walk in site-random environment. We establish precise (sharp) large deviations in the so-called ballistic regime, when the random walk drifts to the right with linear speed. In the…