Model agnostic feature attribution algorithms (such as SHAP and LIME) are ubiquitous techniques for explaining the decisions of complex classification models, such as deep neural networks. However, since complex classification models produce superior performance when trained on low-level (or encoded) features, in many cases, the explanations generated by these algorithms are neither interpretable nor usable by humans. Methods proposed in recent studies that support the generation of human-interpretable explanations are impractical, because they require a fully invertible transformation function that maps the model's input features to the human-interpretable features. In this work, we introduce Latent SHAP, a black-box feature attribution framework that provides human-interpretable explanations, without the requirement for a fully invertible transformation function. We demonstrate Latent SHAP's effectiveness using (1) a controlled experiment where invertible transformation functions are available, which enables robust quantitative evaluation of our method, and (2) celebrity attractiveness classification (using the CelebA dataset) where invertible transformation functions are not available, which enables thorough qualitative evaluation of our method.

High-dimensional linear regression model is the most popular statistical model for high-dimensional data, but it is quite a challenging task to achieve a sparse set of regression coefficients. In this paper, we propose a simple heuristic algorithm to construct sparse high-dimensional linear regression models, which is adapted from the shortest-solution guided decimation algorithm and is referred to as ASSD. This algorithm constructs the support of regression coefficients under the guidance of the shortest least-squares solution of the recursively decimated linear models, and it applies an early-stopping criterion and a second-stage thresholding procedure to refine this support. Our extensive numerical results demonstrate that ASSD outperforms LASSO, adaptive LASSO, vector approximate message passing, and two other representative greedy algorithms in solution accuracy and robustness. ASSD is especially suitable for linear regression problems with highly correlated measurement matrices encountered in real-world applications. Detecting the relationship between a response and a set of predictors is a common problem encountered in different branches of scientific research. This problem is referred to as regression analysis in statistics.

Inverse Problems (IP) might be described as the search of an unknown parameter (that could be a function) that satisfies a given, known equation. Considering the notation: y = A[f] + noise, where f and y are elements of given Hilbert spaces, we would like to compute (or estimate) f given the data y for some level of noise. Typically, IPs are ill-posed in the sense that the solution does not depend continuously on the data. There are several very important and impressive examples of IPs in our daily lives. Medical imaging has been using IPs for decades and it has shaped the area, as for instance, Computerized Tomography (CT) and Magnetic Resonance Imaging (MRI). For an introductory text, see Vogel (2002). A vast literature of IPs is devoted to deterministic problems where the noise term is also a element of a Hilbert space and commonly assumed small in norm, which is not usually verified in practice.

The logistic regression algorithm is a probabilistic machine learning algorithm used for classification tasks. This is usually the first classification algorithm you'll try a classification task on. Unlike many machine learning algorithms that seem to be a black box, the logisitc regression algorithm is easily understood. In this tutorial, you'll learn everything you need to know about the logistic regression algorithm. You'll start by creating a custom logistic regresssion algorithm. This will help you understand everything happening under the hood and how to debug problems with your logisitic regression models. Next, you'll learn how to train and optimize Scikit-Learn implementation of the logistic regression algorithm. Finally, you'll learn how to handle multiclass classification tasks with this algorithm. This tutorial covers L1 and L2 regularization, hyperparameter tuning using grid search, automating machine learning workflow with pipeline, one vs rest classifier, object-oriented programming, modular programming, and documenting Python modules with docstring.

The continuous rise in CO2 emission into the environment is one of the most crucial issues facing the whole world. Many countries are making crucial decisions to control their carbon footprints to escape some of their catastrophic outcomes. There has been a lot of research going on to project the amount of carbon emissions in the future, which can help us to develop innovative techniques to deal with it in advance. Machine learning is one of the most advanced and efficient techniques for predicting the amount of carbon emissions from current data. This paper provides the methods for predicting carbon emissions (CO2 emissions) for the next few years. The predictions are based on data from the past 50 years. The dataset, which is used for making the prediction, is collected from World Bank datasets. This dataset contains CO2 emissions (metric tons per capita) of all the countries from 1960 to 2018. Our method consists of using machine learning techniques to take the idea of what carbon emission measures will look like in the next ten years and project them onto the dataset taken from the World Bank's data repository. The purpose of this research is to compare how different machine learning models (Decision Tree, Linear Regression, Random Forest, and Support Vector Machine) perform on a similar dataset and measure the difference between their predictions.

Objectives: Early detection of liver fibrosis can help cure the disease or prevent disease progression. We perform a comprehensive study of machine learning-based fibrosis detection in CT images using radiomic features to develop a non-invasive approach to fibrosis detection. Methods: Two sets of radiomic features were extracted from spherical ROIs in CT images of 182 patients who underwent simultaneous liver biopsy and CT examinations, one set corresponding to biopsy locations and another distant from biopsy locations. Combinations of contrast, normalization, machine learning model, feature selection method, bin width, and kernel radius were investigated, each of which were trained and evaluated 100 times with randomized development and test cohorts. The best settings were evaluated based on their mean test AUC and the best features were determined based on their frequency among the best settings. Results: Logistic regression models with NC images normalized using Gamma correction with $\gamma = 1.5$ performed best for fibrosis detection. Boruta was the best for radiomic feature selection method. Training a model using these optimal settings and features consisting of first order energy, first order kurtosis, and first order skewness, resulted in a model that achieved mean test AUCs of 0.7549 and 0.7166 on biopsy-based and non-biopsy ROIs respectively, outperforming a baseline and best models found during the initial study. Conclusions: Logistic regression models trained on radiomic features from NC images normalized using Gamma correction with $\gamma = 1.5$ that underwent Boruta feature selection are effective for liver fibrosis detection. Energy, kurtosis, and skewness are particularly effective features for fibrosis detection.

Plotting a learner's generalization performance against the training set size results in a so-called learning curve. This tool, providing insight in the behavior of the learner, is also practically valuable for model selection, predicting the effect of more training data, and reducing the computational complexity of training. We set out to make the (ideal) learning curve concept precise and briefly discuss the aforementioned usages of such curves. The larger part of this survey's focus, however, is on learning curves that show that more data does not necessarily leads to better generalization performance. A result that seems surprising to many researchers in the field of artificial intelligence. We point out the significance of these findings and conclude our survey with an overview and discussion of open problems in this area that warrant further theoretical and empirical investigation.

Differential privacy is the standard privacy definition for performing analyses over sensitive data. Yet, its privacy budget bounds the number of tasks an analyst can perform with reasonable accuracy, which makes it challenging to deploy in practice. This can be alleviated by private sketching, where the dataset is compressed into a single noisy sketch vector which can be shared with the analysts and used to perform arbitrarily many analyses. However, the algorithms to perform specific tasks from sketches must be developed on a case-by-case basis, which is a major impediment to their use. In this paper, we introduce the generic moment-to-moment (M$^2$M) method to perform a wide range of data exploration tasks from a single private sketch. Among other things, this method can be used to estimate empirical moments of attributes, the covariance matrix, counting queries (including histograms), and regression models. Our method treats the sketching mechanism as a black-box operation, and can thus be applied to a wide variety of sketches from the literature, widening their ranges of applications without further engineering or privacy loss, and removing some of the technical barriers to the wider adoption of sketches for data exploration under differential privacy. We validate our method with data exploration tasks on artificial and real-world data, and show that it can be used to reliably estimate statistics and train classification models from private sketches.

Neural networks have shown great predictive power when dealing with various unstructured data such as images and natural languages. The Bayesian neural network captures the uncertainty of prediction by putting a prior distribution for the parameter of the model and computing the posterior distribution. In this paper, we show that the Bayesian neural network using spike-and-slab prior has consistency with nearly minimax convergence rate when the true regression function is in the Besov space. Even when the smoothness of the regression function is unknown the same posterior convergence rate holds and thus the spike-and-slab prior is adaptive to the smoothness of the regression function. We also consider the shrinkage prior, which is more feasible than other priors, and show that it has the same convergence rate. In other words, we propose a practical Bayesian neural network with guaranteed asymptotic properties.

This paper uses computational experiments to explore the role of exposure in the emergence of construction grammars. While usage-based grammars are hypothesized to depend on a learner's exposure to actual language use, the mechanisms of such exposure have only been studied in a few constructions in isolation. This paper experiments with (i) the growth rate of the constructicon, (ii) the convergence rate of grammars exposed to independent registers, and (iii) the rate at which constructions are forgotten when they have not been recently observed. These experiments show that the lexicon grows more quickly than the grammar and that the growth rate of the grammar is not dependent on the growth rate of the lexicon. At the same time, register-specific grammars converge onto more similar constructions as the amount of exposure increases. This means that the influence of specific registers becomes less important as exposure increases. Finally, the rate at which constructions are forgotten when they have not been recently observed mirrors the growth rate of the constructicon. This paper thus presents a computational model of usage-based grammar that includes both the emergence and the unentrenchment of constructions.