Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userStatistical estimation requires unbounded memory
86
0
0.0
(
0
)
Added by
Leonid (Aryeh) Kontorovich
Publication date
2009
fields
Mathematical Statistics
and research's language is
English
Authors
Leonid Kontorovich
Ask ChatGPT about the research
No Arabic abstract
We investigate the existence of bounded-memory consistent estimators of various statistical functionals. This question is resolved in the negative in a rather strong sense. We propose various bounded-memory approximations, using techniques from automata theory and stochastic processes. Some questions of potential interest are raised for future work.
rate research
Read More
When a Genetic Algorithm (GA), or a stochastic algorithm in general, is employed in a statistical problem, the obtained result is affected by both variability due to sampling, that refers to the fact that only a sample is observed, and variability due to the stochastic elements of the algorithm. This topic can be easily set in a framework of statistical and computational tradeoff question, crucial in recent problems, for which statisticians must carefully set statistical and computational part of the analysis, taking account of some resource or time constraints. In the present work we analyze estimation problems tackled by GAs, for which variability of estimates can be decomposed in the two sources of variability, considering some constraints in the form of cost functions, related to both data acquisition and runtime of the algorithm. Simulation studies will be presented to discuss the statistical and computational tradeoff question.
Recently, strong results have been demonstrated by Deep Recurrent Neural Networks on natural language transduction problems. In this paper we explore the representational power of these models using synthetic grammars designed to exhibit phenomena similar to those found in real transduction problems such as machine translation. These experiments lead us to propose new memory-based recurrent networks that implement continuously differentiable analogues of traditional data structures such as Stacks, Queues, and DeQues. We show that these architectures exhibit superior generalisation performance to Deep RNNs and are often able to learn the underlying generating algorithms in our transduction experiments.
Nonparametric statistical tests are useful procedures that can be applied in a wide range of situations, such as testing randomness or goodness of fit, one-sample, two-sample and multiple-sample analysis, association between bivariate samples or count data analysis. Their use is often preferred to parametric tests due to the fact that they require less restrictive assumptions about the population sampled. In this work, JavaNPST, an open source Java library implementing 40 nonparametric statistical tests, is presented. It can be helpful for programmers and practitioners interested in performing nonparametric statistical analyses, providing a quick and easy way of running these tests directly within any Java code. Some examples of use are also shown, highlighting some of the more remarkable capabilities of the library.
This paper considers the problem of cardinality estimation in data stream applications. We present a statistical analysis of probabilistic counting algorithms, focusing on two techniques that use pseudo-random variates to form low-dimensional data sketches. We apply conventional statistical methods to compare probabilistic algorithms based on storing either selected order statistics, or random projections. We derive estimators of the cardinality in both cases, and show that the maximal-term estimator is recursively computable and has exponentially decreasing error bounds. Furthermore, we show that the estimators have comparable asymptotic efficiency, and explain this result by demonstrating an unexpected connection between the two approaches.
This paper introduces a new way to calculate distance-based statistics, particularly when the data are multivariate. The main idea is to pre-calculate the optimal projection directions given the variable dimension, and to project multidimensional variables onto these pre-specified projection directions; by subsequently utilizing the fast algorithm that is developed in Huo and Szekely [2016] for the univariate variables, the computational complexity can be improved from $O(m^2)$ to $O(n m cdot mbox{log}(m))$, where $n$ is the number of projection directions and $m$ is the sample size. When $n ll m/log(m)$, computational savings can be achieved. The key challenge is how to find the optimal pre-specified projection directions. This can be obtained by minimizing the worse-case difference between the true distance and the approximated distance, which can be formulated as a nonconvex optimization problem in a general setting. In this paper, we show that the exact solution of the nonconvex optimization problem can be derived in two special cases: the dimension of the data is equal to either $2$ or the number of projection directions. In the generic settings, we propose an algorithm to find some approximate solutions. Simulations confirm the advantage of our method, in comparison with the pure Monte Carlo approach, in which the directions are randomly selected rather than pre-calculated.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
