Students who take an online course, such as a MOOC, use the course's discussion forum to ask questions or reach out to instructors when encountering an issue. However, reading and responding to students' questions is difficult to scale because of the time needed to consider each message. As a result, critical issues may be left unresolved, and students may lose the motivation to continue in the course. To help address this problem, we build predictive models that automatically determine the urgency of each forum post, so that these posts can be brought to instructors' attention. This paper goes beyond previous work by predicting not just a binary decision cut-off but a post's level of urgency on a 7-point scale. First, we train and cross-validate several models on an original data set of 3,503 posts from MOOCs at University of Pennsylvania. Second, to determine the generalizability of our models, we test their performance on a separate, previously published data set of 29,604 posts from MOOCs at Stanford University. While the previous work on post urgency used only one data set, we evaluated the prediction across different data sets and courses. The best-performing model was a support vector regressor trained on the Universal Sentence Encoder embeddings of the posts, achieving an RMSE of 1.1 on the training set and 1.4 on the test set. Understanding the urgency of forum posts enables instructors to focus their time more effectively and, as a result, better support student learning.

We present a simple linear regression based approach for learning the weights and biases of a neural network, as an alternative to standard gradient based backpropagation. The present work is exploratory in nature, and we restrict the description and experiments to (i) simple feedforward neural networks, (ii) scalar (single output) regression problems, and (iii) invertible activation functions. However, the approach is intended to be extensible to larger, more complex architectures. The key idea is the observation that the input to every neuron in a neural network is a linear combination of the activations of neurons in the previous layer, as well as the parameters (weights and biases) of the layer. If we are able to compute the ideal total input values to every neuron by working backwards from the output, we can formulate the learning problem as a linear least squares problem which iterates between updating the parameters and the activation values. We present an explicit algorithm that implements this idea, and we show that (at least for small problems) the approach is more stable and faster than gradient-based methods.

Surveys are an important research tool, providing unique measurements on subjective experiences such as sentiment and opinions that cannot be measured by other means. However, because survey data is collected from a self-selected group of participants, directly inferring insights from it to a population of interest, or training ML models on such data, can lead to erroneous estimates or under-performing models. In this paper we present balance, an open-source Python package by Meta, offering a simple workflow for analyzing and adjusting biased data samples with respect to a population of interest. The balance workflow includes three steps: understanding the initial bias in the data relative to a target we would like to infer, adjusting the data to correct for the bias by producing weights for each unit in the sample based on propensity scores, and evaluating the final biases and the variance inflation after applying the fitted weights. The package provides a simple API that can be used by researchers and data scientists from a wide range of fields on a variety of data. The paper provides the relevant context, methodological background, and presents the package's API.

Linear Regression is a seminal technique in statistics and machine learning, where the objective is to build linear predictive models between a response (i.e., dependent) variable and one or more predictor (i.e., independent) variables from a given dataset of n instances, where each instance is a set of values of the independent variables and the corresponding value of the dependent variable. One of the classical and widely used approaches is Ordinary Least Square Regression (OLS), where the objective is the minimize the average squared error between the predicted and actual value of the dependent variable. Another classical approach is Quantile Regression (QR), where the objective is to minimize the average weighted absolute error between the predicted and actual value of the dependent variable. QR (also known as "Median Regression" for the special case of the middle quantile), is less affected by outliers and thus statistically a more robust alternative to OLS [15, 18]. However, while there exist efficient algorithms for OLS, the state-of-art algorithms for QR require solving large linear programs with many variables and constraints. They can be solved using using interior point methods [24] which are weakly polynomial (i.e., in the arithmetic computation model the running time is polynomial in the number of bits required to represent the rational numbers in the input), or using Simplex-based exterior point methods which can have exponential time complexity in the worst case [10]. The main focus of our paper is an investigation of the computational complexity of Quantile Regression, and in particular, to design efficient strongly polynomial algorithms (i.e., in the arithmetic computation model the running time is polynomial in the number of rational numbers in the input) for various special cases of the problem.

Machine learning algorithms have become ubiquitous in a number of applications (e.g. image classification). However, due to the insufficient measurement of traditional metrics (e.g. the coarse-grained Accuracy of each classifier), substantial gaps are usually observed between the real-world performance of these algorithms and their scores in standardized evaluations. In this paper, inspired by the psychometric theories from human measurement, we propose a task-agnostic evaluation framework Camilla, where a multi-dimensional diagnostic metric Ability is defined for collaboratively measuring the multifaceted strength of each machine learning algorithm. Specifically, given the response logs from different algorithms to data samples, we leverage cognitive diagnosis assumptions and neural networks to learn the complex interactions among algorithms, samples and the skills (explicitly or implicitly pre-defined) of each sample. In this way, both the abilities of each algorithm on multiple skills and some of the sample factors (e.g. sample difficulty) can be simultaneously quantified. We conduct extensive experiments with hundreds of machine learning algorithms on four public datasets, and our experimental results demonstrate that Camilla not only can capture the pros and cons of each algorithm more precisely, but also outperforms state-of-the-art baselines on the metric reliability, rank consistency and rank stability.

Detection of Volatile Organic Compounds (VOCs) from the breath is becoming a viable route for the early detection of diseases non-invasively. This paper presents a sensor array with three metal oxide electrodes that can use machine learning methods to identify four distinct VOCs in a mixture. The metal oxide sensor array was subjected to various VOC concentrations, including ethanol, acetone, toluene and chloroform. The dataset obtained from individual gases and their mixtures were analyzed using multiple machine learning algorithms, such as Random Forest (RF), K-Nearest Neighbor (KNN), Decision Tree, Linear Regression, Logistic Regression, Naive Bayes, Linear Discriminant Analysis, Artificial Neural Network, and Support Vector Machine. KNN and RF have shown more than 99% accuracy in classifying different varying chemicals in the gas mixtures. In regression analysis, KNN has delivered the best results with R2 value of more than 0.99 and LOD of 0.012, 0.015, 0.014 and 0.025 PPM for predicting the concentrations of varying chemicals Acetone, Toluene, Ethanol, and Chloroform, respectively in complex mixtures. Therefore, it is demonstrated that the array utilizing the provided algorithms can classify and predict the concentrations of the four gases simultaneously for disease diagnosis and treatment monitoring.

In many applications, when building linear regression models, it is important to account for the presence of outliers, i.e., corrupted input data points. Such problems can be formulated as mixed-integer optimization problems involving cubic terms, each given by the product of a binary variable and a quadratic term of the continuous variables. Existing approaches in the literature, typically relying on the linearization of the cubic terms using big-M constraints, suffer from weak relaxation and poor performance in practice. In this work we derive stronger second-order conic relaxations that do not involve big-M constraints. Our computational experiments indicate that the proposed formulations are several orders-of-magnitude faster than existing big-M formulations in the literature for this problem.

Background: Matrix-assisted laser desorption/ionization mass spectrometry imaging (MALDI MSI) displays significant potential for applications in cancer research, especially in tumor typing and subtyping. Lung cancer is the primary cause of tumor-related deaths, where the most lethal entities are adenocarcinoma (ADC) and squamous cell carcinoma (SqCC). Distinguishing between these two common subtypes is crucial for therapy decisions and successful patient management. Results: We propose a new algebraic topological framework, which obtains intrinsic information from MALDI data and transforms it to reflect topological persistence. Our framework offers two main advantages. Firstly, topological persistence aids in distinguishing the signal from noise. Secondly, it compresses the MALDI data, saving storage space and optimizes computational time for subsequent classification tasks. We present an algorithm that efficiently implements our topological framework, relying on a single tuning parameter. Afterwards, logistic regression and random forest classifiers are employed on the extracted persistence features, thereby accomplishing an automated tumor (sub-)typing process. To demonstrate the competitiveness of our proposed framework, we conduct experiments on a real-world MALDI dataset using cross-validation. Furthermore, we showcase the effectiveness of the single denoising parameter by evaluating its performance on synthetic MALDI images with varying levels of noise. Conclusion: Our empirical experiments demonstrate that the proposed algebraic topological framework successfully captures and leverages the intrinsic spectral information from MALDI data, leading to competitive results in classifying lung cancer subtypes. Moreover, the frameworks ability to be fine-tuned for denoising highlights its versatility and potential for enhancing data analysis in MALDI applications.

We consider Bayesian linear regression with sparsity-indu cing prior and design efficient sampling algorithms leveraging posterior contraction properties. A quasi-likelihood with Gaussian spike-and-slab (that is favorable both statistically and computation ally) is investigated and two algorithms based on Gibbs sampling and Stochastic Localization are ana lyzed, both under the same (quite natural) statistical assumptions that also enable valid in ference on the sparse planted signal. The benefit of the Stochastic Localization sampler is particula rly prominent for data matrix that is not well-designed.

The logistic regression model is one of the most popular data generation model in noisy binary classification problems. In this work, we study the sample complexity of estimating the parameters of the logistic regression model up to a given $\ell_2$ error, in terms of the dimension and the inverse temperature, with standard normal covariates. The inverse temperature controls the signal-to-noise ratio of the data generation process. While both generalization bounds and asymptotic performance of the maximum-likelihood estimator for logistic regression are well-studied, the non-asymptotic sample complexity that shows the dependence on error and the inverse temperature for parameter estimation is absent from previous analyses. We show that the sample complexity curve has two change-points (or critical points) in terms of the inverse temperature, clearly separating the low, moderate, and high temperature regimes.