Related papers: The strong predictable representation property in …

We explore various combinatorial problems mostly borrowed from physics, that share the property of being continuously or discretely integrable, a feature that guarantees the existence of conservation laws that often make the problems…

Let $M =(M_t)_{t\geq 0}$ be any continuous real-valued stochastic process. We prove that if there exists a sequence $(a_n)_{n\geq 1}$ of real numbers which converges to 0 and such that $M$ satisfies the reflection property at all levels…

The inference of deep hierarchical models is problematic due to strong dependencies between the hierarchies. We investigate a specific transformation of the model parameters based on the multivariate distributional transform. This…

Deep neural networks come in many sizes and architectures. The choice of architecture, in conjunction with the dataset and learning algorithm, is commonly understood to affect the learned neural representations. Yet, recent results have…

We develop a theoretical approach to compute the conditioned spectral density of $N \times N$ non-invariant random matrices in the limit $N \rightarrow \infty$. This large deviation observable, defined as the eigenvalue distribution…

Adaptive behavior often requires predicting future events. The theory of reinforcement learning prescribes what kinds of predictive representations are useful and how to compute them. This paper integrates these theoretical ideas with work…

In this paper we study progressive filtration expansions with c\`adl\`ag processes. Using results from the theory of the weak convergence of $\sigma$-fields, we first establish a semimartingale convergence theorem. Then we apply it in a…

In causal models, a given mechanism is assumed to be invariant to changes of other mechanisms. While this principle has been utilized for inference in settings where the causal variables are observed, theoretical insights when the variables…

Pathwise predictability of continuous time processes is studied in deterministic setting. We discuss uniform prediction in some weak sense with respect to certain classes of inputs. More precisely, we study possibility of approximation of…

The classic model of computable randomness considers martingales that take real or rational values. Recent work by Bienvenu et al. (2012) and Teutsch (2014) shows that fundamental features of the classic model change when the martingales…

Recent works have argued that high-level semantic concepts are encoded "linearly" in the representation space of large language models. In this work, we study the origins of such linear representations. To that end, we introduce a simple…

A substantial generalisation is put forward of the theory of subjective fiducial inference as it was outlined in earlier papers. In particular, this theory is extended to deal with cases where the data are discrete or categorical rather…

We investigate the density large deviation function for a multidimensional conservation law in the vanishing viscosity limit, when the probability concentrates on weak solutions of a hyperbolic conservation law conservation law. When the…

We extend the framework of variational autoencoders to represent transformations explicitly in the latent space. In the family of hierarchical graphical models that emerges, the latent space is populated by higher order objects that are…

It is well-known that well-posedness of a martingale problem in the class of continuous (or r.c.l.l.) solutions enables one to construct the associated transition probability functions. We extend this result to the case when the martingale…

We formulate and analyze an inverse problem using derivatives prices to obtain an implied filtering density on volatility's hidden state. Stochastic volatility is the unobserved state in a hidden Markov model (HMM) and can be tracked using…

We prove a fiberwise almost sure invariance principle for random piecewise expanding transformations in one and higher dimensions using recent developments on martingale techniques.

When light from a distant source object, like a galaxy or a supernova, travels towards us, it is deflected by massive objects that lie on its path. When the mass density of the deflecting object exceeds a certain threshold, multiple, highly…

The sub-linear expectation space is a nonlinear expectation space having advantages of modelling the uncertainty of probability and distribution. In the sub-linear expectation space, we use capacity and sub-linear expectation to replace…

In the previous papers (Kui\'{c} et al. in Found Phys 42:319-339, 2012; Kui\'{c} in arXiv:1506.02622, 2015), it was demonstrated that applying the principle of maximum information entropy by maximizing the conditional information entropy,…