Related papers: Linear classifier, least-squares cost function, an…
Latest least squares regression (LSR) methods mainly try to learn slack regression targets to replace strict zero-one labels. However, the difference of intra-class targets can also be highlighted when enlarging the distance between…
The least squares method allows fitting parameters of a mathematical model from experimental data. This article proposes a general approach of this method. After introducing the method and giving a formal definition, the transitivity of the…
In this paper we provide a definition of pattern of outliers in contingency tables within a model-based framework. In particular, we make use of log-linear models and exact goodness-of-fit tests to specify the notions of outlier and pattern…
Clustering problems are well-studied in a variety of fields such as data science, operations research, and computer science. Such problems include variants of centre location problems, $k$-median, and $k$-means to name a few. In some cases,…
Regression analysis is an important instrument to determine the effect of the explanatory variables on response variables. When outliers and bias errors are present, the standard weighted least squares estimator may perform poorly. For this…
The output scores of a neural network classifier are converted to probabilities via normalizing over the scores of all competing categories. Computing this partition function, $Z$, is then linear in the number of categories, which is…
In this paper, we consider a statistical problem of learning a linear model from noisy samples. Existing work has focused on approximating the least squares solution by using leverage-based scores as an importance sampling distribution.…
Partially linear additive models generalize linear ones since they model the relation between a response variable and covariates by assuming that some covariates have a linear relation with the response but each of the others enter through…
Matrix-variate distributions are a recent addition to the model-based clustering field, thereby making it possible to analyze data in matrix form with complex structure such as images and time series. Due to its recent appearance, there is…
In many astronomical problems one often needs to determine the upper and/or lower boundary of a given data set. An automatic and objective approach consists in fitting the data using a generalised least-squares method, where the function to…
This paper deals with a linear model of regression on quantiles when the explanatory variable takes values in some functional space and the response is scalar. We propose a spline estimator of the functional coefficient that minimizes a…
The partial least squares procedure was originally developed to estimate the slope parameter in multivariate parametric models. More recently it has gained popularity in the functional data literature. There, the partial least squares…
We propose to address the common problem of linear estimation in linear statistical models by using a model selection approach via penalization. Depending then on the framework in which the linear statistical model is considered namely the…
Real-world datasets often contain outliers, and the presence of outliers can make the clustering problems to be much more challenging. In this paper, we propose a simple uniform sampling framework for solving three representative…
The cost-sensitive classification problem plays a crucial role in mission-critical machine learning applications, and differs with traditional classification by taking the misclassification costs into consideration. Although being studied…
We derive closed formulas for the condition number of a linear function of the total least squares solution. Given an over determined linear system Ax=b, we show that this condition number can be computed using the singular values and the…
In a corpus of data, outliers are either errors: mistakes in the data that are counterproductive, or are unique: informative samples that improve model robustness. Identifying outliers can lead to better datasets by (1) removing noise in…
Principal component analysis (PCA) is widely used for dimensionality reduction, with well-documented merits in various applications involving high-dimensional data, including computer vision, preference measurement, and bioinformatics. In…
This paper studies the problem of robustly learning the correlation function for a univariate time series with the presence of noise, outliers and missing entries. The outliers or anomalies considered here are sparse and rare events that…
Impulsed noise outliers are data points that differs significantly from other observations.They are generally removed from the data set through local regression or Kalman filter algorithm.However, these methods, or their generalizations,…