Robust Maximum Likelihood Estimation of Sparse Vector Error Correction Model

arXiv.org Machine Learning

In econometrics and finance, the vector error correction model (VECM) is an important time series model for cointegration analysis, which is used to estimate the long-run equilibrium variable relationships. The traditional analysis and estimation methodologies assume the underlying Gaussian distribution but, in practice, heavy-tailed data and outliers can lead to the inapplicability of these methods. In this paper, we propose a robust model estimation method based on the Cauchy distribution to tackle this issue. In addition, sparse cointegration relations are considered to realize feature selection and dimension reduction. An efficient algorithm based on the majorization-minimization (MM) method is applied to solve the proposed nonconvex problem. The performance of this algorithm is shown through numerical simulations.


Designing communication systems via iterative improvement: error correction coding with Bayes decoder and codebook optimized for source symbol error

arXiv.org Artificial Intelligence

In error correction coding (ECC), the typical error metric is the bit error rate (BER) which measures the number of bit errors. For this metric, the positions of the bits are not relevant to the decoding, and in many noise models, not relevant to the BER either. In many applications this is unsatisfactory as typically all bits are not equal and have different significance. We look at ECC from a Bayesian perspective and introduce Bayes estimators with general loss functions to take into account the bit significance. We propose ECC schemes that optimize this error metric. As the problem is highly nonlinear, traditional ECC construction techniques are not applicable and we use iterative improvement search techniques to find good codebooks. We provide numerical experiments to show that they can be superior to classical linear block codes such as Hamming codes and decoding methods such as minimum distance decoding.


Software for Data Mining, Analytics,Data Science, and Knowledge Discovery

AITopics Original Links

Classification software: building models to separate 2 or more discrete classes using Multiple methods Decision Tree Rules Neural Bayesian SVM Genetic, Rough Sets, Fuzzy Logic and other approaches Analysis of results, ROC Social Network Analysis, Link Analysis, and Visualization software Text Analysis, Text Mining, and Information Retrieval (IR) Web Analytics and Social Media Analytics software. BI (Business Intelligence), Database and OLAP software Data Transformation, Data Cleaning, Data Cleansing Libraries, Components and Developer Kits for creating embedded data mining applications Web Content Mining, web scraping, screen scraping.


Convex Approaches to Model Wavelet Sparsity Patterns

arXiv.org Machine Learning

Statistical dependencies among wavelet coefficients are commonly represented by graphical models such as hidden Markov trees(HMTs). However, in linear inverse problems such as deconvolution, tomography, and compressed sensing, the presence of a sensing or observation matrix produces a linear mixing of the simple Markovian dependency structure. This leads to reconstruction problems that are non-convex optimizations. Past work has dealt with this issue by resorting to greedy or suboptimal iterative reconstruction methods. In this paper, we propose new modeling approaches based on group-sparsity penalties that leads to convex optimizations that can be solved exactly and efficiently. We show that the methods we develop perform significantly better in deconvolution and compressed sensing applications, while being as computationally efficient as standard coefficient-wise approaches such as lasso.


Generalised Propagation for Fast Fourier Transforms with Partial or Missing Data

Neural Information Processing Systems

Discrete Fourier transforms and other related Fourier methods have been practically implementable due to the fast Fourier transform (FFT). However there are many situations where doing fast Fourier transforms without complete data would be desirable. In this paper itis recognised that formulating the FFT algorithm as a belief network allows suitable priors to be set for the Fourier coefficients. Furthermore efficient generalised belief propagation methods between clustersof four nodes enable the Fourier coefficients to be inferred and the missing data to be estimated in near to O(n log n) time, where n is the total of the given and missing data points. This method is compared with a number of common approaches such as setting missing data to zero or to interpolation. It is tested on generated data and for a Fourier analysis of a damaged audio signal.