Understanding how feature learning affects generalization is among the foremost goals of modern deep learning theory. Here, we study how the ability to learn representations affects the generalization performance of a simple class of models: deep Bayesian linear neural networks trained on unstructured Gaussian data. By comparing deep random feature models to deep networks in which all layers are trained, we provide a detailed characterization of the interplay between width, depth, data density, and prior mismatch. We show that both models display sample-wise double-descent behavior in the presence of label noise. Random feature models can also display model-wise double-descent if there are narrow bottleneck layers, while deep networks do not show these divergences. Random feature models can have particular widths that are optimal for generalization at a given data density, while making neural networks as wide or as narrow as possible is always optimal. Moreover, we show that the leading-order correction to the kernel-limit learning curve cannot distinguish between random feature models and deep networks in which all layers are trained. Taken together, our findings begin to elucidate how architectural details affect generalization performance in this simple class of deep regression models.

Convert a molecule from the SMILES string to an rdkit object 3.2.2. Working with the rdkit object 3.2.3. Convert list of molecules to rdkit object 3.3.

The classical Cox model emerged in 1972 promoting breakthroughs in how patient prognosis is quantified using time-to-event analysis in biomedicine. One of the most useful characteristics of the model for practitioners is the interpretability of the variables in the analysis. However, this comes at the price of introducing strong assumptions concerning the functional form of the regression model. To break this gap, this paper aims to exploit the explainability advantages of the classical Cox model in the setting of interval-censoring using a new Lasso neural network that simultaneously selects the most relevant variables while quantifying non-linear relations between predictors and survival times. The gain of the new method is illustrated empirically in an extensive simulation study with examples that involve linear and non-linear ground dependencies. We also demonstrate the performance of our strategy in the analysis of physiological, clinical and accelerometer data from the NHANES 2003-2006 waves to predict the effect of physical activity on the survival of patients. Our method outperforms the prior results in the literature that use the traditional Cox model.

This paper studies the multi-task high-dimensional linear regression models where the noise among different tasks is correlated, in the moderately high dimensional regime where sample size $n$ and dimension $p$ are of the same order. Our goal is to estimate the covariance matrix of the noise random vectors, or equivalently the correlation of the noise variables on any pair of two tasks. Treating the regression coefficients as a nuisance parameter, we leverage the multi-task elastic-net and multi-task lasso estimators to estimate the nuisance. By precisely understanding the bias of the squared residual matrix and by correcting this bias, we develop a novel estimator of the noise covariance that converges in Frobenius norm at the rate $n^{-1/2}$ when the covariates are Gaussian. This novel estimator is efficiently computable. Under suitable conditions, the proposed estimator of the noise covariance attains the same rate of convergence as the "oracle" estimator that knows in advance the regression coefficients of the multi-task model. The Frobenius error bounds obtained in this paper also illustrate the advantage of this new estimator compared to a method-of-moments estimator that does not attempt to estimate the nuisance. As a byproduct of our techniques, we obtain an estimate of the generalization error of the multi-task elastic-net and multi-task lasso estimators. Extensive simulation studies are carried out to illustrate the numerical performance of the proposed method.

Unstructured data, especially text, continues to grow rapidly in various domains. In particular, in the financial sphere, there is a wealth of accumulated unstructured financial data, such as the textual disclosure documents that companies submit on a regular basis to regulatory agencies, such as the Securities and Exchange Commission (SEC). These documents are typically very long and tend to contain valuable soft information about a company's performance. It is therefore of great interest to learn predictive models from these long textual documents, especially for forecasting numerical key performance indicators (KPIs). Whereas there has been a great progress in pre-trained language models (LMs) that learn from tremendously large corpora of textual data, they still struggle in terms of effective representations for long documents. Our work fills this critical need, namely how to develop better models to extract useful information from long textual documents and learn effective features that can leverage the soft financial and risk information for text regression (prediction) tasks. In this paper, we propose and implement a deep learning framework that splits long documents into chunks and utilizes pre-trained LMs to process and aggregate the chunks into vector representations, followed by self-attention to extract valuable document-level features. We evaluate our model on a collection of 10-K public disclosure reports from US banks, and another dataset of reports submitted by US companies. Overall, our framework outperforms strong baseline methods for textual modeling as well as a baseline regression model using only numerical data. Our work provides better insights into how utilizing pre-trained domain-specific and fine-tuned long-input LMs in representing long documents can improve the quality of representation of textual data, and therefore, help in improving predictive analyses.

Laser machining is a highly flexible non-contact manufacturing technique that has been employed widely across academia and industry. Due to nonlinear interactions between light and matter, simulation methods are extremely crucial, as they help enhance the machining quality by offering comprehension of the inter-relationships between the laser processing parameters. On the other hand, experimental processing parameter optimization recommends a systematic, and consequently time-consuming, investigation over the available processing parameter space. An intelligent strategy is to employ machine learning (ML) techniques to capture the relationship between picosecond laser machining parameters for finding proper parameter combinations to create the desired cuts on industrial-grade alumina ceramic with deep, smooth and defect-free patterns. Laser parameters such as beam amplitude and frequency, scanner passing speed and the number of passes over the surface, as well as the vertical distance of the scanner from the sample surface, are used for predicting the depth, top width, and bottom width of the engraved channels using ML models. Owing to the complex correlation between laser parameters, it is shown that Neural Networks (NN) are the most efficient in predicting the outputs. Equipped with an ML model that captures the interconnection between laser parameters and the engraved channel dimensions, one can predict the required input parameters to achieve a target channel geometry. This strategy significantly reduces the cost and effort of experimental laser machining during the development phase, without compromising accuracy or performance. The developed techniques can be applied to a wide range of ceramic laser machining processes.

This article aims to propose and apply a machine learning method to analyze the direction of returns from Exchange Traded Funds (ETFs) using the historical return data of its components, helping to make investment strategy decisions through a trading algorithm. In methodological terms, regression and classification models were applied, using standard datasets from Brazilian and American markets, in addition to algorithmic error metrics. In terms of research results, they were analyzed and compared to those of the Na\"ive forecast and the returns obtained by the buy & hold technique in the same period of time. In terms of risk and return, the models mostly performed better than the control metrics, with emphasis on the linear regression model and the classification models by logistic regression, support vector machine (using the LinearSVC model), Gaussian Naive Bayes and K-Nearest Neighbors, where in certain datasets the returns exceeded by two times and the Sharpe ratio by up to four times those of the buy & hold control model.

Linear regression is a regression model which outputs a numeric value. It is used to predict an outcome based on a linear set of input. As you can guess this function represents a linear line in the coordinate system. The hypothesis function (h0) approximates the output given input. A linear regression model can either represent a univariate or a multivariate problem.

In our case study on analyzing sentiment, you will create models that predict a class (positive/negative sentiment) from input features (text of the reviews, user profile information,...). In our second case study for this course, loan default prediction, you will tackle financial data, and predict when a loan is likely to be risky or safe for the bank. These tasks are an examples of classification, one of the most widely used areas of machine learning, with a broad array of applications, including ad targeting, spam detection, medical diagnosis and image classification. In this course, you will create classifiers that provide state-of-the-art performance on a variety of tasks. You will become familiar with the most successful techniques, which are most widely used in practice, including logistic regression, decision trees and boosting.

Image Classification is a process of classifying various image categories to their appropriate labels or categories it is associated with. Image classification is mostly employed with Convolutional Neural Networks (CNNs), but this article is an attempt to showcase that even logistic regression has the capability to classify images efficiently with a reduction in computational time and also to waive off the tedious task of building complex models for image classification. Logistic Regression is one of the supervised machine learning algorithms which would be majorly employed for binary class classification problems where according to the occurrence of a particular category of data the outcomes are fixed. Logistic regression operates basically through a sigmoidal function for values ranging between 0 and 1. As mentioned earlier as this article emphasizes using Logistic Regression for Image classification we are using the Hand Sign Digit Classification dataset with two categories of images showing Hand Signs of 0 and 1.