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 Statistical Learning


Artificial Intelligence Drives the Archaeological Discoveries of Stone Age

#artificialintelligence

Machine learning model and Neural Networks helps in extracting archaic information about human civilization. Archaeology is the gateway to our past. It describes events which shaped the world how it is today and the transition that led humans from animal-hunter to a knowledgeable-mosaic. In archaeology, Stone Age holds the key relevance. It establishes the patterns of human behavior and helps in identifying the transitions that hurled humans to the path of development.


The Solution to a Data Science Problem is not Unique

#artificialintelligence

Data science projects vary in scope and complexity. Sometimes, the project could be as simple as producing summary statistics, charts, and visualizations. It could also involve building a regression model, classification model, or forecasting using a time-dependent dataset. The project could also be very complex and difficult, with no clear guidance as to the specific type of model to use. In this case, it is the task of the data science aspirant or professional to come up with a model that best suitable for addressing project goals and objectives.


Timeline for Data Science Competence

#artificialintelligence

For anyone interested in jumping into the field of data science, one of the most important questions to ask is: How long does it take to gain competency in data science? This article will discuss the typical timeline for data science competency. The time required to gain competency in data science depends on the level of competency. In Section II, we will discuss the three levels of data science. In Section III, we discuss the time required for gaining data science competency based on the level of interest.


Machine Learning Algorithms: Everything You Need to Know - Business Module Hub

#artificialintelligence

If you're an AI professional or aspire to be one, one thing you must be aware of is: machine learning algorithms are your closest aid and ally. These algorithms can also be annoying. Given that there is a multitude of algorithms. The knowledge of algorithms is essential to be an effective AI engineer, data scientist, and machine learning engineer. To give you a gist of how these algorithms work, let's get down to know these algorithms.


Flow-Based Likelihoods for Non-Gaussian Inference

arXiv.org Machine Learning

We investigate the use of data-driven likelihoods to bypass a key assumption made in many scientific analyses, which is that the true likelihood of the data is Gaussian. In particular, we suggest using the optimization targets of flow-based generative models, a class of models that can capture complex distributions by transforming a simple base distribution through layers of nonlinearities. We call these flow-based likelihoods (FBL). We analyze the accuracy and precision of the reconstructed likelihoods on mock Gaussian data, and show that simply gauging the quality of samples drawn from the trained model is not a sufficient indicator that the true likelihood has been learned. We nevertheless demonstrate that the likelihood can be reconstructed to a precision equal to that of sampling error due to a finite sample size. We then apply FBLs to mock weak lensing convergence power spectra, a cosmological observable that is significantly non-Gaussian (NG). We find that the FBL captures the NG signatures in the data extremely well, while other commonly used data-driven likelihoods, such as Gaussian mixture models and independent component analysis, fail to do so. This suggests that works that have found small posterior shifts in NG data with data-driven likelihoods such as these could be underestimating the impact of non-Gaussianity in parameter constraints. By introducing a suite of tests that can capture different levels of NG in the data, we show that the success or failure of traditional data-driven likelihoods can be tied back to the structure of the NG in the data. Unlike other methods, the flexibility of the FBL makes it successful at tackling different types of NG simultaneously. Because of this, and consequently their likely applicability across datasets and domains, we encourage their use for inference when sufficient mock data are available for training.


Variational (Gradient) Estimate of the Score Function in Energy-based Latent Variable Models

arXiv.org Machine Learning

The learning and evaluation of energy-based latent variable models (EBLVMs) without any structural assumptions are highly challenging, because the true posteriors and the partition functions in such models are generally intractable. This paper presents variational estimates of the score function and its gradient with respect to the model parameters in a general EBLVM, referred to as VaES and VaGES respectively. The variational posterior is trained to minimize a certain divergence to the true model posterior and the bias in both estimates can be bounded by the divergence theoretically. With a minimal model assumption, VaES and VaGES can be applied to the kernelized Stein discrepancy (KSD) and score matching (SM)-based methods to learn EBLVMs. Besides, VaES can also be used to estimate the exact Fisher divergence between the data and general EBLVMs.


Trust Issues: Uncertainty Estimation Does Not Enable Reliable OOD Detection On Medical Tabular Data

arXiv.org Artificial Intelligence

When deploying machine learning models in high-stakes real-world environments such as health care, it is crucial to accurately assess the uncertainty concerning a model's prediction on abnormal inputs. However, there is a scarcity of literature analyzing this problem on medical data, especially on mixed-type tabular data such as Electronic Health Records. We close this gap by presenting a series of tests including a large variety of contemporary uncertainty estimation techniques, in order to determine whether they are able to identify out-of-distribution (OOD) patients. In contrast to previous work, we design tests on realistic and clinically relevant OOD groups, and run experiments on real-world medical data. We find that almost all techniques fail to achieve convincing results, partly disagreeing with earlier findings.


Curse of Small Sample Size in Forecasting of the Active Cases in COVID-19 Outbreak

arXiv.org Machine Learning

During the COVID-19 pandemic, a massive number of attempts on the predictions of the number of cases and the other future trends of this pandemic have been made. However, they fail to predict, in a reliable way, the medium and long term evolution of fundamental features of COVID-19 outbreak within acceptable accuracy. This paper gives an explanation for the failure of machine learning models in this particular forecasting problem. The paper shows that simple linear regression models provide high prediction accuracy values reliably but only for a 2-weeks period and that relatively complex machine learning models, which have the potential of learning long term predictions with low errors, cannot achieve to obtain good predictions with possessing a high generalization ability. It is suggested in the paper that the lack of a sufficient number of samples is the source of low prediction performance of the forecasting models. The reliability of the forecasting results about the active cases is measured in terms of the cross-validation prediction errors, which are used as expectations for the generalization errors of the forecasters. To exploit the information, which is of most relevant with the active cases, we perform feature selection over a variety of variables. We apply different feature selection methods, namely the Pairwise Correlation, Recursive Feature Selection, and feature selection by using the Lasso regression and compare them to each other and also with the models not employing any feature selection. Furthermore, we compare Linear Regression, Multi-Layer Perceptron, and Long-Short Term Memory models each of which is used for prediction active cases together with the mentioned feature selection methods. Our results show that the accurate forecasting of the active cases with high generalization ability is possible up to 3 days only because of the small sample size of COVID-19 data.


Settling the Robust Learnability of Mixtures of Gaussians

arXiv.org Machine Learning

This work represents a natural coalescence of two important lines of work: learning mixtures of Gaussians and algorithmic robust statistics. In particular we give the first provably robust algorithm for learning mixtures of any constant number of Gaussians. We require only mild assumptions on the mixing weights (bounded fractionality) and that the total variation distance between components is bounded away from zero. At the heart of our algorithm is a new method for proving dimension-independent polynomial identifiability through applying a carefully chosen sequence of differential operations to certain generating functions that not only encode the parameters we would like to learn but also the system of polynomial equations we would like to solve. We show how the symbolic identities we derive can be directly used to analyze a natural sum-of-squares relaxation.


Ridge Regression with Frequent Directions: Statistical and Optimization Perspectives

arXiv.org Machine Learning

Despite its impressive theory \& practical performance, Frequent Directions (\acrshort{fd}) has not been widely adopted for large-scale regression tasks. Prior work has shown randomized sketches (i) perform worse in estimating the covariance matrix of the data than \acrshort{fd}; (ii) incur high error when estimating the bias and/or variance on sketched ridge regression. We give the first constant factor relative error bounds on the bias \& variance for sketched ridge regression using \acrshort{fd}. We complement these statistical results by showing that \acrshort{fd} can be used in the optimization setting through an iterative scheme which yields high-accuracy solutions. This improves on randomized approaches which need to compromise the need for a new sketch every iteration with speed of convergence. In both settings, we also show using \emph{Robust Frequent Directions} further enhances performance.