Related papers: Taxonomy of Prediction
A theory of recursive and corecursive definitions has been developed in higher-order logic (HOL) and mechanized using Isabelle. Least fixedpoints express inductive data types such as strict lists; greatest fixedpoints express coinductive…
Symbolic dynamics has proven to be an invaluable tool in analyzing the mechanisms that lead to unpredictability and random behavior in nonlinear dynamical systems. Surprisingly, a discrete partition of continuous state space can produce a…
Orthogonal polynomial approximations form the foundation to a set of well-established methods for uncertainty quantification known as polynomial chaos. These approximations deliver models for emulating physical systems in a variety of…
Our understanding of complex systems rests on our ability to characterise how they perform distributed computation and integrate information. Advances in information theory have introduced several quantities to describe complex information…
The idea is advanced that self-organization in complex systems can be treated as decision making (as it is performed by humans) and, vice versa, decision making is nothing but a kind of self-organization in the decision maker nervous…
Network or graph structures are ubiquitous in the study of complex systems. Often, we are interested in complexity trends of these system as it evolves under some dynamic. An example might be looking at the complexity of a food web as…
This work introduces a notion of approximate probabilistic trace equivalence for labelled Markov chains, and relates this new concept to the known notion of approximate probabilistic bisimulation. In particular this work shows that the…
Bidirectional typing is a discipline in which the typing judgment is decomposed explicitly into inference and checking modes, allowing to control the flow of type information in typing rules and to specify algorithmically how they should be…
We propose and analyze a novel theoretical and algorithmic framework for structured prediction. While so far the term has referred to discrete output spaces, here we consider more general settings, such as manifolds or spaces of probability…
Human behavior has the nature of indeterminacy, which requires the pedestrian trajectory prediction system to model the multi-modality of future motion states. Unlike existing stochastic trajectory prediction methods which usually use a…
Model uncertainty is pervasive in real world analysis situations and is an often-neglected issue in applied statistics. However, standard approaches to the research process do not address the inherent uncertainty in model building and,…
Diffusion models are loosely modelled based on non-equilibrium thermodynamics, where \textit{diffusion} refers to particles flowing from high-concentration regions towards low-concentration regions. In statistics, the meaning is quite…
Learning from the multidimensional data has been an interesting concept in the field of machine learning. However, such learning can be difficult, complex, expensive because of expensive data processing, manipulations as the number of…
A biform theory is a combination of an axiomatic theory and an algorithmic theory that supports the integration of reasoning and computation. These are ideal for specifying and reasoning about algorithms that manipulate mathematical…
It is well known that text compression can be achieved by predicting the next symbol in the stream of text data based on the history seen up to the current symbol. The better the prediction the more skewed the conditional probability…
The true process that generated data cannot be determined when multiple explanations are possible. Prediction requires a model of the probability that a process, chosen randomly from the set of candidate explanations, generates some future…
Can we infer sources of errors from outputs of the complex data analytics software? Bidirectional programming promises that we can reverse flow of software, and translate corrections of output into corrections of either input or data…
A discrete-time stochastic process derived from a model of basketball is used to generalize any discrete distribution. The generalized distributions can have one or two more parameters than the parent distribution. Those derived from…
We consider the problem of performing inference with imprecise continuous-time hidden Markov chains, that is, imprecise continuous-time Markov chains that are augmented with random output variables whose distribution depends on the hidden…
We examine data-processing of Markov chains through the lens of information geometry. We first establish a theory of congruent Markov morphisms within the framework of stochastic matrices. Specifically, we introduce and justify the concept…