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"Computational learning theory Statistical methods."
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Pandemic velocity: Forecasting COVID-19 in the US with a machine learning & Bayesian time series compartmental model
Predictions of COVID-19 case growth and mortality are critical to the decisions of political leaders, businesses, and individuals grappling with the pandemic. This predictive task is challenging due to the novelty of the virus, limited data, and dynamic political and societal responses. We embed a Bayesian time series model and a random forest algorithm within an epidemiological compartmental model for empirically grounded COVID-19 predictions. The Bayesian case model fits a location-specific curve to the velocity (first derivative) of the log transformed cumulative case count, borrowing strength across geographic locations and incorporating prior information to obtain a posterior distribution for case trajectories. The compartmental model uses this distribution and predicts deaths using a random forest algorithm trained on COVID-19 data and population-level characteristics, yielding daily projections and interval estimates for cases and deaths in U.S. states. We evaluated the model by training it on progressively longer periods of the pandemic and computing its predictive accuracy over 21-day forecasts. The substantial variation in predicted trajectories and associated uncertainty between states is illustrated by comparing three unique locations: New York, Colorado, and West Virginia. The sophistication and accuracy of this COVID-19 model offer reliable predictions and uncertainty estimates for the current trajectory of the pandemic in the U.S. and provide a platform for future predictions as shifting political and societal responses alter its course.
Journal Article
Subgrid modelling for two-dimensional turbulence using neural networks
In this investigation, a data-driven turbulence closure framework is introduced and deployed for the subgrid modelling of Kraichnan turbulence. The novelty of the proposed method lies in the fact that snapshots from high-fidelity numerical data are used to inform artificial neural networks for predicting the turbulence source term through localized grid-resolved information. In particular, our proposed methodology successfully establishes a map between inputs given by stencils of the vorticity and the streamfunction along with information from two well-known eddy-viscosity kernels. Through this we predict the subgrid vorticity forcing in a temporally and spatially dynamic fashion. Our study is both a priori and a posteriori in nature. In the former, we present an extensive hyper-parameter optimization analysis in addition to learning quantification through probability-density-function-based validation of subgrid predictions. In the latter, we analyse the performance of our framework for flow evolution in a classical decaying two-dimensional turbulence test case in the presence of errors related to temporal and spatial discretization. Statistical assessments in the form of angle-averaged kinetic energy spectra demonstrate the promise of the proposed methodology for subgrid quantity inference. In addition, it is also observed that some measure of a posteriori error must be considered during optimal model selection for greater accuracy. The results in this article thus represent a promising development in the formalization of a framework for generation of heuristic-free turbulence closures from data.
Journal Article
Learning and Expectations in Macroeconomics
A crucial challenge for economists is figuring out how people interpret the world and form expectations that will likely influence their economic activity. Inflation, asset prices, exchange rates, investment, and consumption are just some of the economic variables that are largely explained by expectations. Here George Evans and Seppo Honkapohja bring new explanatory power to a variety of expectation formation models by focusing on the learning factor. Whereas the rational expectations paradigm offers the prevailing method to determining expectations, it assumes very theoretical knowledge on the part of economic actors. Evans and Honkapohja contribute to a growing body of research positing that households and firms learn by making forecasts using observed data, updating their forecast rules over time in response to errors. This book is the first systematic development of the new statistical learning approach.
Depending on the particular economic structure, the economy may converge to a standard rational-expectations or a \"rational bubble\" solution, or exhibit persistent learning dynamics. The learning approach also provides tools to assess the importance of new models with expectational indeterminacy, in which expectations are an independent cause of macroeconomic fluctuations. Moreover, learning dynamics provide a theory for the evolution of expectations and selection between alternative equilibria, with implications for business cycles, asset price volatility, and policy. This book provides an authoritative treatment of this emerging field, developing the analytical techniques in detail and using them to synthesize and extend existing research.
eBook
OPTIMAL COMPUTATIONAL AND STATISTICAL RATES OF CONVERGENCE FOR SPARSE NONCONVEX LEARNING PROBLEMS
We provide theoretical analysis of the statistical and computational properties of penalized M-estimators that can be formulated as the solution to a possibly nonconvex optimization problem. Many important estimators fall in this category, including least squares regression with nonconvex regularization, generalized linear models with nonconvex regularization and sparse elliptical random design regression. For these problems, it is intractable to calculate the global solution due to the nonconvex formulation. In this paper, we propose an approximate regularization path-following method for solving a variety of learning problems with nonconvex objective functions. Under a unified analytic framework, we simultaneously provide explicit statistical and computational rates of convergence for any local solution attained by the algorithm. Computationally, our algorithm attains a global geometric rate of convergence for calculating the full regularization path, which is optimal among all first-order algorithms. Unlike most existing methods that only attain geometric rates of convergence for one single regularization parameter, our algorithm calculates the full regularization path with the same iteration complexity. In particular, we provide a refined iteration complexity bound to sharply characterize the performance of each stage along the regularization path. Statistically, we provide sharp sample complexity analysis for all the approximate local solutions along the regularization path. In particular, our analysis improves upon existing results by providing a more refined sample complexity bound as well as an exact support recovery result for the final estimator. These results show that the final estimator attains an oracle statistical property due to the usage of nonconvex penalty.
Journal Article
Strong rules for discarding predictors in lasso-type problems
We consider rules for discarding predictors in lasso regression and related problems, for computational efficiency. El Ghaoui and his colleagues have proposed 'SAFE' rules, based on univariate inner products between each predictor and the outcome, which guarantee that a coefficient will be 0 in the solution vector. This provides a reduction in the number of variables that need to be entered into the optimization. We propose strong rules that are very simple and yet screen out far more predictors than the SAFE rules. This great practical improvement comes at a price: the strong rules are not foolproof and can mistakenly discard active predictors, i.e. predictors that have non-zero coefficients in the solution. We therefore combine them with simple checks of the Karush-Kuhn-Tucker conditions to ensure that the exact solution to the convex problem is delivered. Of course, any (approximate) screening method can be combined with the Karush-Kuhn-Tucker conditions to ensure the exact solution; the strength of the strong rules lies in the fact that, in practice, they discard a very large number of the inactive predictors and almost never commit mistakes. We also derive conditions under which they are foolproof. Strong rules provide substantial savings in computational time for a variety of statistical optimization problems.
Journal Article
A hybrid CNN-LSTM model for typhoon formation forecasting
A typhoon is an extreme weather event that can cause huge loss of life and economic damage in coastal areas and beyond. As a consequence, the search for more accurate predictive models of typhoon formation; and, intensity have become imperative as meteorologists, governments, and other agencies seek to mitigate the impact of these catastrophic events. While work in this field has progressed diligently, this paper argues, that the existing models are deficient. Traditional numerical forecast models based on fluid mechanics have difficulty in predicting the intensity of typhoons. Forecasts based on statistics and machine learning fail to take into account the spatial and temporal relationships among typhoon formation variables leading to weaknesses in the predictive power of this model. Therefore, we propose a hybrid model, which we argue, can produce a more realist and accurate account of typhoon ‘behavior’ as it focuses on both the spatio-temporal correlations of atmospheric and oceanographic variables. Our CNN-LSTM model introduces 3D convolutional neural networks (3DCNN) and 2D convolutional neural networks (2DCNN) as a method to better understand the spatial relationships of the features of typhoon formation. We also use LSTM to examine the temporal sequence of relations in typhoon progression. Extensive experiments based on three datasets show that our hybrid CNN-LSTM model is superior to existing methods, including numerical forecast models used by many official organizations; and, statistical forecast and machine learning based methods.
Journal Article
Learning probability distributions of sensory inputs with Monte Carlo predictive coding
It has been suggested that the brain employs probabilistic generative models to optimally interpret sensory information. This hypothesis has been formalised in distinct frameworks, focusing on explaining separate phenomena. On one hand, classic predictive coding theory proposed how the probabilistic models can be learned by networks of neurons employing local synaptic plasticity. On the other hand, neural sampling theories have demonstrated how stochastic dynamics enable neural circuits to represent the posterior distributions of latent states of the environment. These frameworks were brought together by variational filtering that introduced neural sampling to predictive coding. Here, we consider a variant of variational filtering for static inputs, to which we refer as Monte Carlo predictive coding (MCPC). We demonstrate that the integration of predictive coding with neural sampling results in a neural network that learns precise generative models using local computation and plasticity. The neural dynamics of MCPC infer the posterior distributions of the latent states in the presence of sensory inputs, and can generate likely inputs in their absence. Furthermore, MCPC captures the experimental observations on the variability of neural activity during perceptual tasks. By combining predictive coding and neural sampling, MCPC can account for both sets of neural data that previously had been explained by these individual frameworks.
Journal Article
Deep learning approaches for detecting DDoS attacks: a systematic review
In today’s world, technology has become an inevitable part of human life. In fact, during the Covid-19 pandemic, everything from the corporate world to educational institutes has shifted from offline to online. It leads to exponential increase in intrusions and attacks over the Internet-based technologies. One of the lethal threat surfacing is the Distributed Denial of Service (DDoS) attack that can cripple down Internet-based services and applications in no time. The attackers are updating their skill strategies continuously and hence elude the existing detection mechanisms. Since the volume of data generated and stored has increased manifolds, the traditional detection mechanisms are not appropriate for detecting novel DDoS attacks. This paper systematically reviews the prominent literature specifically in deep learning to detect DDoS. The authors have explored four extensively used digital libraries (IEEE, ACM, ScienceDirect, Springer) and one scholarly search engine (Google scholar) for searching the recent literature. We have analyzed the relevant studies and the results of the SLR are categorized into five main research areas: (i) the different types of DDoS attack detection deep learning approaches, (ii) the methodologies, strengths, and weaknesses of existing deep learning approaches for DDoS attacks detection (iii) benchmarked datasets and classes of attacks in datasets used in the existing literature, and (iv) the preprocessing strategies, hyperparameter values, experimental setups, and performance metrics used in the existing literature (v) the research gaps, and future directions.
Journal Article
GRAMEP: an alignment-free method based on the maximum entropy principle for identifying SNPs
Background
Advances in high throughput sequencing technologies provide a huge number of genomes to be analyzed. Thus, computational methods play a crucial role in analyzing and extracting knowledge from the data generated. Investigating genomic mutations is critical because of their impact on chromosomal evolution, genetic disorders, and diseases. It is common to adopt aligning sequences for analyzing genomic variations. However, this approach can be computationally expensive and restrictive in scenarios with large datasets.
Results
We present a novel method for identifying single nucleotide polymorphisms (SNPs) in DNA sequences from assembled genomes. This study proposes GRAMEP, an alignment-free approach that adopts the principle of maximum entropy to discover the most informative k-mers specific to a genome or set of sequences under investigation. The informative k-mers enable the detection of variant-specific mutations in comparison to a reference genome or other set of sequences. In addition, our method offers the possibility of classifying novel sequences with no need for organism-specific information. GRAMEP demonstrated high accuracy in both in silico simulations and analyses of viral genomes, including Dengue, HIV, and SARS-CoV-2. Our approach maintained accurate SARS-CoV-2 variant identification while demonstrating a lower computational cost compared to methods with the same purpose.
Conclusions
GRAMEP is an open and user-friendly software based on maximum entropy that provides an efficient alignment-free approach to identifying and classifying unique genomic subsequences and SNPs with high accuracy, offering advantages over comparative methods. The instructions for use, applicability, and usability of GRAMEP are open access at
https://github.com/omatheuspimenta/GRAMEP
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Journal Article