Compression and Conditional Emulation of Climate Model Output

Numerical climate model simulations run at high spatial and temporal resolutions generate massive quantities of data. As our computing capabilities continue to increase, storing all of the data is not sustainable, and thus it is important to develop methods for representing the full datasets by smaller compressed versions. We propose a statistical compression and decompression algorithm based on storing a set of summary statistics as well as a statistical model describing the conditional distribution of the full dataset given the summary statistics. The statistical model can be used to generate realizations representing the full dataset, along with characterizations of the uncertainties in the generated data. Thus, the methods are capable of both compression and conditional emulation of the climate models. Considerable attention is paid to accurately modeling the original dataset--one year of daily mean temperature data--particularly with regard to the inherent spatial nonstationarity in global fields, and to determining the statistics to be stored, so that the variation in the original data can be closely captured, while allowing for fast decompression and conditional emulation on modest computers

Estimating the Algorithmic Complexity of Stock Markets

Randomness and regularities in Finance are usually treated in probabilistic terms. In this paper, we develop a completely different approach in using a non-probabilistic framework based on the algorithmic information theory initially developed by Kolmogorov (1965). We present some elements of this theory and show why it is particularly relevant to Finance, and potentially to other sub-fields of Economics as well. We develop a generic method to estimate the Kolmogorov complexity of numeric series. This approach is based on an iterative "regularity erasing procedure" implemented to use lossless compression algorithms on financial data. Examples are provided with both simulated and real-world financial time series. The contributions of this article are twofold. The first one is methodological : we show that some structural regularities, invisible with classical statistical tests, can be detected by this algorithmic method. The second one consists in illustrations on the daily Dow-Jones Index suggesting that beyond several well-known regularities, hidden structure may in this index remain to be identified

High Dimensional Classification with combined Adaptive Sparse PLS and Logistic Regression

Motivation: The high dimensionality of genomic data calls for the development of specific classification methodologies, especially to prevent over-optimistic predictions. This challenge can be tackled by compression and variable selection, which combined constitute a powerful framework for classification, as well as data visualization and interpretation. However, current proposed combinations lead to instable and non convergent methods due to inappropriate computational frameworks. We hereby propose a stable and convergent approach for classification in high dimensional based on sparse Partial Least Squares (sparse PLS). Results: We start by proposing a new solution for the sparse PLS problem that is based on proximal operators for the case of univariate responses. Then we develop an adaptive version of the sparse PLS for classification, which combines iterative optimization of logistic regression and sparse PLS to ensure convergence and stability. Our results are confirmed on synthetic and experimental data. In particular we show how crucial convergence and stability can be when cross-validation is involved for calibration purposes. Using gene expression data we explore the prediction of breast cancer relapse. We also propose a multicategorial version of our method on the prediction of cell-types based on single-cell expression data. Availability: Our approach is implemented in the plsgenomics R-package.Comment: 9 pages, 3 figures, 4 tables + Supplementary Materials 8 pages, 3 figures, 10 table

IDENTIFICATION OF COVER SONGS USING INFORMATION THEORETIC MEASURES OF SIMILARITY

13 pages, 5 figures, 4 tables. v3: Accepted version13 pages, 5 figures, 4 tables. v3: Accepted version13 pages, 5 figures, 4 tables. v3: Accepted versio

Approximations of Algorithmic and Structural Complexity Validate Cognitive-behavioural Experimental Results

We apply methods for estimating the algorithmic complexity of sequences to behavioural sequences of three landmark studies of animal behavior each of increasing sophistication, including foraging communication by ants, flight patterns of fruit flies, and tactical deception and competition strategies in rodents. In each case, we demonstrate that approximations of Logical Depth and Kolmogorv-Chaitin complexity capture and validate previously reported results, in contrast to other measures such as Shannon Entropy, compression or ad hoc. Our method is practically useful when dealing with short sequences, such as those often encountered in cognitive-behavioural research. Our analysis supports and reveals non-random behavior (LD and K complexity) in flies even in the absence of external stimuli, and confirms the "stochastic" behaviour of transgenic rats when faced that they cannot defeat by counter prediction. The method constitutes a formal approach for testing hypotheses about the mechanisms underlying animal behaviour.Comment: 28 pages, 7 figures and 2 table