Related papers: MaxEnt Queries and Sequential Sampling
All measurements of continuous signals rely on taking discrete snapshots, with the Nyquist-Shannon theorem dictating sampling paradigms. We present a broader framework of information-optimal measurement, showing that traditional sampling is…
We study Bayesian optimal control of a general class of smoothly parameterized Markov decision problems. Since computing the optimal control is computationally expensive, we design an algorithm that trades off performance for computational…
We propose a novel sequence prediction method for sequential data capturing node traversals in graphs. Our method builds on a statistical modelling framework that combines multiple higher-order network models into a single multi-order…
We consider the problem of estimating confidence intervals for the mean of a random variable, where the goal is to produce the smallest possible interval for a given number of samples. While minimax optimal algorithms are known for this…
We investigate the problem of jointly testing two hypotheses and estimating a random parameter based on data that is observed sequentially by sensors in a distributed network. In particular, we assume the data to be drawn from a Gaussian…
Effective resource allocation in sensor networks, IoT systems, and distributed computing is essential for applications such as environmental monitoring, surveillance, and smart infrastructure. Sensors or agents must optimize their resource…
The present work shows that the maximum-entropy method can be applied to a sample of neuronal recordings along two different routes: (1) apply to the sample; or (2) apply to a larger, unsampled neuronal population from which the sample is…
This paper considers a set of sensors, which as a group are tasked with taking measurements of the environment and sending a small subset of the measurements to a centralized data fusion center, where the measurements will be used to…
We explore a data-driven approach for learning to optimize neural networks. We construct a dataset of neural network checkpoints and train a generative model on the parameters. In particular, our model is a conditional diffusion transformer…
In this paper, we propose an optimization-based mechanism to explain power law distributions, where the function that the optimization process is seeking to optimize is derived mathematically, then the behavior and interpretation of this…
A distributed consensus algorithm for estimating the maximum value of the initial measurements in a sensor network with communication noise is proposed. In the absence of communication noise, max estimation can be done by updating the state…
Sampling is a fundamental technique, and sampling without replacement is often desirable when duplicate samples are not beneficial. Within machine learning, sampling is useful for generating diverse outputs from a trained model. We present…
Optimisation problems in science and engineering typically involve finding the ground state (i.e. the minimum energy configuration) of a cost function with respect to many variables. If the variables are corrupted by noise then this…
The scientific method relies on the iterated processes of inference and inquiry. The inference phase consists of selecting the most probable models based on the available data; whereas the inquiry phase consists of using what is known about…
We discuss how the method of maximum entropy, MaxEnt, can be extended beyond its original scope, as a rule to assign a probability distribution, to a full-fledged method for inductive inference. The main concept is the (relative) entropy…
The method of maximum entropy (ME) is extended to address the following problem: Once one accepts that the ME distribution is to be preferred over all others, the question is to what extent are distributions with lower entropy supposed to…
We consider optimal stopping problems, in which a sequence of independent random variables is drawn from a known continuous density. The objective of such problems is to find a procedure which maximizes the expected reward; this is often…
We consider sequential hypothesis testing between two quantum states using adaptive and non-adaptive strategies. In this setting, samples of an unknown state are requested sequentially and a decision to either continue or to accept one of…
Semi-continuous data comes from a distribution that is a mixture of the point mass at zero and a continuous distribution with support on the positive real line. A clear example is the daily rainfall data. In this paper, we present a novel…
We construct the generalized entropy optimized by a given arbitrary statistical distribution with a finite linear expectation value of a random quantity of interest. This offers, via the maximum entropy principle, a unified basis for a…