Related papers: Parameter Estimation of Heavy-Tailed AR Model with…
Advances in artificial intelligence (AI) and deep learning have led to neural networks being used to generate lightning-speed answers to complex science questions, paintings in the style of Monet, or stories like those of Twain. Leveraging…
In this paper I present a new approach for regression of time series using their own samples. This is a celebrated problem known as Auto-Regression. Dealing with outlier or missed samples in a time series makes the problem of estimation…
[This paper was initially published in PHME conference in 2016, selected for further publication in International Journal of Prognostics and Health Management.] This paper describes an Autoregressive Partially-hidden Markov model (ARPHMM)…
The horseshoe prior is known to possess many desirable properties for Bayesian estimation of sparse parameter vectors, yet its density function lacks an analytic form. As such, it is challenging to find a closed-form solution for the…
This paper tackles the problem of robust covariance matrix estimation when the data is incomplete. Classical statistical estimation methodologies are usually built upon the Gaussian assumption, whereas existing robust estimation ones assume…
Autoregressive (AR) models have been the dominating approach to conditional sequence generation, but are suffering from the issue of high inference latency. Non-autoregressive (NAR) models have been recently proposed to reduce the latency…
Mixed linear regression (MLR) model is among the most exemplary statistical tools for modeling non-linear distributions using a mixture of linear models. When the additive noise in MLR model is Gaussian, Expectation-Maximization (EM)…
Time series are used in many domains including finance, engineering, economics and bioinformatics generally to represent the change of a measurement over time. Modeling techniques may then be used to give a synthetic representation of such…
The Student-$t$ distribution is widely used in statistical modeling of datasets involving outliers since its longer-than-normal tails provide a robust approach to hand such data. Furthermore, data collected over time may contain censored or…
We express the classic ARMA time-series model as a directed graphical model. In doing so, we find that the deterministic relationships in the model make it effectively impossible to use the EM algorithm for learning model parameters. To…
We develop an unsupervised mixture model for non-negative, skewed and heavy-tailed data, such as losses in actuarial and risk management applications. The mixture has a lognormal component, which is usually appropriate for the body of the…
Recently, high-dimensional heterogeneous data have attracted a lot of attention and discussion. Under heterogeneity, semiparametric regression is a popular choice to model data in statistics. In this paper, we take advantages of expectile…
Anomaly detection on time series data is increasingly common across various industrial domains that monitor metrics in order to prevent potential accidents and economic losses. However, a scarcity of labeled data and ambiguous definitions…
Equalisation Maximisation (EqM) is an algorithm for estimating parameters in auto-regressive (AR) models where some fraction of the data is missing. It has previously been shown that the EqM algorithm is a competitive alternative to…
We propose an algorithm to impute and forecast a time series by transforming the observed time series into a matrix, utilizing matrix estimation to recover missing values and de-noise observed entries, and performing linear regression to…
Logistic regression is a common classification method in supervised learning. Surprisingly, there are very few solutions for performing logistic regression with missing values in the covariates. We suggest a complete approach based on a…
We study an EM algorithm for estimating product-term regression models with missing data. The study of such problems in the likelihood tradition has thus far been restricted to an EM algorithm method using full numerical integration.…
Large sample statistical analysis of threshold autoregressive (TAR) models is usually based on the assumption that the underlying driving noise is uncorrelated. In this paper, we consider a model, driven by Gaussian noise with geometric…
We propose an $\ell_1$-penalized estimator for high-dimensional models of Expected Shortfall (ES). The estimator is obtained as the solution to a least-squares problem for an auxiliary dependent variable, which is defined as a…
We present a compartmentalized approach to finding the maximum a-posteriori (MAP) estimate of a latent time series that obeys a dynamic stochastic model and is observed through noisy measurements. We specifically consider modern signal…