Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userInferring the conditional mean
443
0
0.0
(
0
)
Added by
Gusztav Morvai
Publication date
2007
fields
Informatics Engineering
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
Consider a stationary real-valued time series ${X_n}_{n=0}^{infty}$ with a priori unknown distribution. The goal is to estimate the conditional expectation $E(X_{n+1}|X_0,..., X_n)$ based on the observations $(X_0,..., X_n)$ in a pointwise consistent way. It is well known that this is not possible at all values of $n$. We will estimate it along stopping times.
rate research
Read More
Information diffusion is a fundamental process that takes place over networks. While it is rarely realistic to observe the individual transmissions of the information diffusion process, it is typically possible to observe when individuals first publish the information. We look specifically at previously published algorithm NETINF that probabilistically identifies the optimal network that best explains the observed infection times. We explore how the algorithm could perform on a range of intrinsically different social and information network topologies, from news blogs and websites to Twitter to Reddit.
Recently a new quantum generalization of the Renyi divergence and the corresponding conditional Renyi entropies was proposed. Here we report on a surprising relation between conditional Renyi entropies based on this new generalization and conditional Renyi entropies based on the quantum relative Renyi entropy that was used in previous literature. Our result generalizes the well-known duality relation H(A|B) + H(A|C) = 0 of the conditional von Neumann entropy for tripartite pure states to Renyi entropies of two different kinds. As a direct application, we prove a collection of inequalities that relate different conditional Renyi entropies and derive a new entropic uncertainty relation.
The behaviour of many real-world phenomena can be modelled by nonlinear dynamical systems whereby a latent system state is observed through a filter. We are interested in interacting subsystems of this form, which we model by a set of coupled maps as a synchronous update graph dynamical systems. Specifically, we study the structure learning problem for spatially distributed dynamical systems coupled via a directed acyclic graph. Unlike established structure learning procedures that find locally maximum posterior probabilities of a network structure containing latent variables, our work exploits the properties of dynamical systems to compute globally optimal approximations of these distributions. We arrive at this result by the use of time delay embedding theorems. Taking an information-theoretic perspective, we show that the log-likelihood has an intuitive interpretation in terms of information transfer.
Conditional Mutual Information (CMI) is a measure of conditional dependence between random variables X and Y, given another random variable Z. It can be used to quantify conditional dependence among variables in many data-driven inference problems such as graphical models, causal learning, feature selection and time-series analysis. While k-nearest neighbor (kNN) based estimators as well as kernel-based methods have been widely used for CMI estimation, they suffer severely from the curse of dimensionality. In this paper, we leverage advances in classifiers and generative models to design methods for CMI estimation. Specifically, we introduce an estimator for KL-Divergence based on the likelihood ratio by training a classifier to distinguish the observed joint distribution from the product distribution. We then show how to construct several CMI estimators using this basic divergence estimator by drawing ideas from conditional generative models. We demonstrate that the estimates from our proposed approaches do not degrade in performance with increasing dimension and obtain significant improvement over the widely used KSG estimator. Finally, as an application of accurate CMI estimation, we use our best estimator for conditional independence testing and achieve superior performance than the state-of-the-art tester on both simulated and real data-sets.
The decision tree is one of the most fundamental programming abstractions. A commonly used type of decision tree is the alphabetic binary tree, which uses (without loss of generality) ``less than versus greater than or equal to tests in order to determine one of $n$ outcome events. The process of finding an optimal alphabetic binary tree for a known probability distribution on outcome events usually has the underlying assumption that the cost (time) per decision is uniform and thus independent of the outcome of the decision. This assumption, however, is incorrect in the case of software to be optimized for a given microprocessor, e.g., in compiling switch statements or in fine-tuning program bottlenecks. The operation of the microprocessor generally means that the cost for the more likely decision outcome can or will be less -- often far less -- than the less likely decision outcome. Here we formulate a variety of $O(n^3)$-time $O(n^2)$-space dynamic programming algorithms to solve such optimal binary decision tree problems, optimizing for the behavior of processors with predictive branch capabilities, both static and dynamic. In the static case, we use existing results to arrive at entropy-based performance bounds. Solutions to this formulation are often faster in practice than ``optimal decision trees as formulated in the literature, and, for small problems, are easily worth the extra complexity in finding the better solution. This can be applied in fast implementation of decoding Huffman codes.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
