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Exploring the impact of post-training rounding in regression models

Jan Kalina (2024)

Applications of Mathematics

Post-training rounding, also known as quantization, of estimated parameters stands as a widely adopted technique for mitigating energy consumption and latency in machine learning models. This theoretical endeavor delves into the examination of the impact of rounding estimated parameters in key regression methods within the realms of statistics and machine learning. The proposed approach allows for the perturbation of parameters through an additive error with values within a specified interval. This...

Exponential inequalities for VLMC empirical trees

Antonio Galves, Véronique Maume-Deschamps, Bernard Schmitt (2008)

ESAIM: Probability and Statistics

A seminal paper by Rissanen, published in 1983, introduced the class of Variable Length Markov Chains and the algorithm Context which estimates the probabilistic tree generating the chain. Even if the subject was recently considered in several papers, the central question of the rate of convergence of the algorithm remained open. This is the question we address here. We provide an exponential upper bound for the probability of incorrect estimation of the probabilistic tree, as a function...

Exponential smoothing and resampling techniques in time series prediction

Maria Manuela Neves, Clara Cordeiro (2010)

Discussiones Mathematicae Probability and Statistics

Time series analysis deals with records that are collected over time. The objectives of time series analysis depend on the applications, but one of the main goals is to predict future values of the series. These values depend, usually in a stochastic manner, on the observations available at present. Such dependence has to be considered when predicting the future from its past, taking into account trend, seasonality and other features of the data. Some of the most successful forecasting methods are...

Exponential smoothing based on L-estimation

Přemysl Bejda, Tomáš Cipra (2015)

Kybernetika

Robust methods similar to exponential smoothing are suggested in this paper. First previous results for exponential smoothing in L 1 are generalized using the regression quantiles, including a generalization to more parameters. Then a method based on the classical sign test is introduced that should deal not only with outliers but also with level shifts, including a detection of change points. Properties of various approaches are investigated by means of a simulation study. A real data example is...

Exponential smoothing for irregular data

Tomáš Cipra (2006)

Applications of Mathematics

Various types of exponential smoothing for data observed at irregular time intervals are surveyed. Double exponential smoothing and some modifications of Holt’s method for this type of data are suggested. A real data example compares double exponential smoothing and Wright’s modification of Holt’s method for data observed at irregular time intervals.

Exponential smoothing for irregular time series

Tomáš Cipra, Tomáš Hanzák (2008)

Kybernetika

The paper deals with extensions of exponential smoothing type methods for univariate time series with irregular observations. An alternative method to Wright’s modification of simple exponential smoothing based on the corresponding ARIMA process is suggested. Exponential smoothing of order m for irregular data is derived. A similar method using a DLS **discounted least squares** estimation of polynomial trend of order m is derived as well. Maximum likelihood parameters estimation for forecasting...

Exponential smoothing for time series with outliers

Tomáš Hanzák, Tomáš Cipra (2011)

Kybernetika

Recursive time series methods are very popular due to their numerical simplicity. Their theoretical background is usually based on Kalman filtering in state space models (mostly in dynamic linear systems). However, in time series practice one must face frequently to outlying values (outliers), which require applying special methods of robust statistics. In the paper a simple robustification of Kalman filter is suggested using a simple truncation of the recursive residuals. Then this concept is applied...

Extraction of fuzzy logic rules from data by means of artificial neural networks

Martin Holeňa (2005)

Kybernetika

The extraction of logical rules from data has been, for nearly fifteen years, a key application of artificial neural networks in data mining. Although Boolean rules have been extracted in the majority of cases, also methods for the extraction of fuzzy logic rules have been studied increasingly often. In the paper, those methods are discussed within a five-dimensional classification scheme for neural-networks based rule extraction, and it is pointed out that all of them share the feature of being...

Extrapolation in fractional autoregressive models

Jiří Anděl, Georg Neuhaus (1998)

Kybernetika

The naïve and the least-squares extrapolation are investigated in the fractional autoregressive models of the first order. Some explicit formulas are derived for the one and two steps ahead extrapolation.

Extrapolations in non-linear autoregressive processes

Jiří Anděl, Václav Dupač (1999)

Kybernetika

We derive a formula for m -step least-squares extrapolation in non-linear AR ( p ) processes and compare it with the naïve extrapolation. The least- squares extrapolation depends on the distribution of white noise. Some bounds for it are derived that depend only on the expectation of white noise. An example shows that in general case the difference between both types of extrapolation can be very large. Further, a formula for least-squares extrapolation in multidimensional non-linear AR( p ) process is derived....

Extremal behaviour of stationary processes: the calibration technique in the extremal index estimation

D. Prata Gomes, Maria Manuela Neves (2010)

Discussiones Mathematicae Probability and Statistics

Classical extreme value methods were derived when the underlying process is assumed to be a sequence of independent random variables. However when observations are taken along the time and/or the space the independence is an unrealistic assumption. A parameter that arises in this situation, characterizing the degree of local dependence in the extremes of a stationary series, is the extremal index, θ. In several areas such as hydrology, telecommunications, finance and environment, for example, the...

Extreme values and kernel estimates of point processes boundaries

Stéphane Girard, Pierre Jacob (2004)

ESAIM: Probability and Statistics

We present a method for estimating the edge of a two-dimensional bounded set, given a finite random set of points drawn from the interior. The estimator is based both on a Parzen-Rosenblatt kernel and extreme values of point processes. We give conditions for various kinds of convergence and asymptotic normality. We propose a method of reducing the negative bias and edge effects, illustrated by some simulations.

Extreme values and kernel estimates of point processes boundaries

Stéphane Girard, Pierre Jacob (2010)

ESAIM: Probability and Statistics

We present a method for estimating the edge of a two-dimensional bounded set, given a finite random set of points drawn from the interior. The estimator is based both on a Parzen-Rosenblatt kernel and extreme values of point processes. We give conditions for various kinds of convergence and asymptotic normality. We propose a method of reducing the negative bias and edge effects, illustrated by some simulations.

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