Integer-Forcing Source Coding

Integer-Forcing (IF) is a new framework, based on compute-and-forward, for decoding multiple integer linear combinations from the output of a Gaussian multiple-input multiple-output channel. This work applies the IF approach to arrive at a new low-complexity scheme, IF source coding, for distributed lossy compression of correlated Gaussian sources under a minimum mean squared error distortion measure. All encoders use the same nested lattice codebook. Each encoder quantizes its observation using the fine lattice as a quantizer and reduces the result modulo the coarse lattice, which plays the role of binning. Rather than directly recovering the individual quantized signals, the decoder first recovers a full-rank set of judiciously chosen integer linear combinations of the quantized signals, and then inverts it. In general, the linear combinations have smaller average powers than the original signals. This allows to increase the density of the coarse lattice, which in turn translates to smaller compression rates. We also propose and analyze a one-shot version of IF source coding, that is simple enough to potentially lead to a new design principle for analog-to-digital converters that can exploit spatial correlations between the sampled signals.Comment: Submitted to IEEE Transactions on Information Theor

The Maximum Lq-Likelihood Method: an Application to Extreme Quantile Estimation in Finance

Estimating financial risk is a critical issue for banks and insurance companies. Recently, quantile estimation based on Extreme Value Theory (EVT) has found a successful domain of application in such a context, outperforming other approaches. Given a parametric model provided by EVT, a natural approach is Maximum Likelihood estimation. Although the resulting estimator is asymptotically efficient, often the number of observations available to estimate the parameters of the EVT models is too small in order to make the large sample property trustworthy. In this paper, we study a new estimator of the parameters, the Maximum Lq-Likelihood estimator (MLqE), introduced by Ferrari and Yang (2007). We show that the MLqE can outperform the standard MLE, when estimating tail probabilities and quantiles of the Generalized Extreme Value (GEV) and the Generalized Pareto (GP) distributions. First, we assess the relative efficiency between the the MLqE and the MLE for various sample sizes, using Monte Carlo simulations. Second, we analyze the performance of the MLqE for extreme quantile estimation using real-world financial data. The MLqE is characterized by a distortion parameter q and extends the traditional log-likelihood maximization procedure. When q→1, the new estimator approaches the traditionalMaximum Likelihood Estimator (MLE), recovering its desirable asymptotic properties; when q 6=1 and the sample size is moderate or small, the MLqE successfully trades bias for variance, resulting in an overall gain in terms of accuracy (Mean Squared Error).Maximum Likelihood, Extreme Value Theory, q-Entropy, Tail-related Risk Measures

The Maximum Lq-Likelihood Method: an Application to Extreme Quantile Estimation in Finance

Estimating financial risk is a critical issue for banks and insurance companies. Recently, quantile estimation based on Extreme Value Theory (EVT) has found a successful domain of application in such a context, outperforming other approaches. Given a parametric model provided by EVT, a natural approach is Maximum Likelihood estimation. Although the resulting estimator is asymptotically efficient, often the number of observations available to estimate the parameters of the EVT models is too small in order to make the large sample property trustworthy. In this paper, we study a new estimator of the parameters, the Maximum Lq-Likelihood estimator (MLqE), introduced by Ferrari and Yang (2007). We show that the MLqE can outperform the standard MLE, when estimating tail probabilities and quantiles of the Generalized Extreme Value (GEV) and the Generalized Pareto (GP) distributions. First, we assess the relative efficiency between the the MLqE and the MLE for various sample sizes, using Monte Carlo simulations. Second, we analyze the performance of the MLqE for extreme quantile estimation using real-world financial data. The MLqE is characterized by a distortion parameter q and extends the traditional log-likelihood maximization procedure. When q?1, the new estimator approaches the traditionalMaximum Likelihood Estimator (MLE), recovering its desirable asymptotic properties; when q 6=1 and the sample size is moderate or small, the MLqE successfully trades bias for variance, resulting in an overall gain in terms of accuracy (Mean Squared Error).Maximum Likelihood, Extreme Value Theory, q-Entropy, Tail-related Risk Measures

A mask-based approach for the geometric calibration of thermal-infrared cameras

Accurate and efficient thermal-infrared (IR) camera calibration is important for advancing computer vision research within the thermal modality. This paper presents an approach for geometrically calibrating individual and multiple cameras in both the thermal and visible modalities. The proposed technique can be used to correct for lens distortion and to simultaneously reference both visible and thermal-IR cameras to a single coordinate frame. The most popular existing approach for the geometric calibration of thermal cameras uses a printed chessboard heated by a flood lamp and is comparatively inaccurate and difficult to execute. Additionally, software toolkits provided for calibration either are unsuitable for this task or require substantial manual intervention. A new geometric mask with high thermal contrast and not requiring a flood lamp is presented as an alternative calibration pattern. Calibration points on the pattern are then accurately located using a clustering-based algorithm which utilizes the maximally stable extremal region detector. This algorithm is integrated into an automatic end-to-end system for calibrating single or multiple cameras. The evaluation shows that using the proposed mask achieves a mean reprojection error up to 78% lower than that using a heated chessboard. The effectiveness of the approach is further demonstrated by using it to calibrate two multiple-camera multiple-modality setups. Source code and binaries for the developed software are provided on the project Web site

Maximum Lqq-likelihood estimation

In this paper, the maximum L$q$-likelihood estimator (ML$q$E), a new parameter estimator based on nonextensive entropy [Kibernetika 3 (1967) 30--35] is introduced. The properties of the ML$q$E are studied via asymptotic analysis and computer simulations. The behavior of the ML$q$E is characterized by the degree of distortion $q$ applied to the assumed model. When $q$ is properly chosen for small and moderate sample sizes, the ML$q$E can successfully trade bias for precision, resulting in a substantial reduction of the mean squared error. When the sample size is large and $q$ tends to 1, a necessary and sufficient condition to ensure a proper asymptotic normality and efficiency of ML$q$E is established.Comment: Published in at http://dx.doi.org/10.1214/09-AOS687 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Pairwise Quantization

We consider the task of lossy compression of high-dimensional vectors through quantization. We propose the approach that learns quantization parameters by minimizing the distortion of scalar products and squared distances between pairs of points. This is in contrast to previous works that obtain these parameters through the minimization of the reconstruction error of individual points. The proposed approach proceeds by finding a linear transformation of the data that effectively reduces the minimization of the pairwise distortions to the minimization of individual reconstruction errors. After such transformation, any of the previously-proposed quantization approaches can be used. Despite the simplicity of this transformation, the experiments demonstrate that it achieves considerable reduction of the pairwise distortions compared to applying quantization directly to the untransformed data