A key assumption in multiple scientific applications is that the distribution of observed data can be modeled by a latent tree graphical model. An important example is phylogenetics, where the tree models the evolutionary lineages of various organisms. Given a set of independent realizations of the random variables at the leaves of the tree, a common task is to infer the underlying tree topology. In this work we develop Spectral Neighbor Joining (SNJ), a novel method to recover latent tree graphical models. In contrast to distance based methods, SNJ is based on a spectral measure of similarity between all pairs of observed variables. We prove that SNJ is consistent, and derive a sufficient condition for correct tree recovery from an estimated similarity matrix. Combining this condition with a concentration of measure result on the similarity matrix, we bound the number of samples required to recover the tree with high probability. We illustrate via extensive simulations that SNJ requires fewer samples to accurately recover trees in regimes where the tree contains a large number of leaves or long edges. We provide theoretical support for this observation by analyzing the model of a perfect binary tree.

Clustering is a popular form of unsupervised learning for geometric data. Unfortunately, many clustering algorithms lead to cluster assignments that are hard to explain, partially because they depend on all the features of the data in a complicated way. To improve interpretability, we consider using a small decision tree to partition a data set into clusters, so that clusters can be characterized in a straightforward manner. We study this problem from a theoretical viewpoint, measuring cluster quality by the $k$-means and $k$-medians objectives: Must there exist a tree-induced clustering whose cost is comparable to that of the best unconstrained clustering, and if so, how can it be found? In terms of negative results, we show, first, that popular top-down decision tree algorithms may lead to clusterings with arbitrarily large cost, and second, that any tree-induced clustering must in general incur an $\Omega(\log k)$ approximation factor compared to the optimal clustering. On the positive side, we design an efficient algorithm that produces explainable clusters using a tree with $k$ leaves. For two means/medians, we show that a single threshold cut suffices to achieve a constant factor approximation, and we give nearly-matching lower bounds. For general $k \geq 2$, our algorithm is an $O(k)$ approximation to the optimal $k$-medians and an $O(k^2)$ approximation to the optimal $k$-means. Prior to our work, no algorithms were known with provable guarantees independent of dimension and input size.

Today, machine learning (ML) models are increasingly applied in decision making. This induces an urgent need for quality assurance of ML models with respect to (often domain-dependent) requirements. Monotonicity is one such requirement. It specifies a software as 'learned' by an ML algorithm to give an increasing prediction with the increase of some attribute values. While there exist multiple ML algorithms for ensuring monotonicity of the generated model, approaches for checking monotonicity, in particular of black-box models, are largely lacking. In this work, we propose verification-based testing of monotonicity, i.e., the formal computation of test inputs on a white-box model via verification technology, and the automatic inference of this approximating white-box model from the black-box model under test. On the white-box model, the space of test inputs can be systematically explored by a directed computation of test cases. The empirical evaluation on 90 black-box models shows verification-based testing can outperform adaptive random testing as well as property-based techniques with respect to effectiveness and efficiency.

Imputation of missing data is a common application in various classification problems where the feature training matrix has missingness. A widely used solution to this imputation problem is based on the lazy learning technique, $k$-nearest neighbor (kNN) approach. However, most of the previous work on missing data does not take into account the presence of the class label in the classification problem. Also, existing kNN imputation methods use variants of Minkowski distance as a measure of distance, which does not work well with heterogeneous data. In this paper, we propose a novel iterative kNN imputation technique based on class weighted grey distance between the missing datum and all the training data. Grey distance works well in heterogeneous data with missing instances. The distance is weighted by Mutual Information (MI) which is a measure of feature relevance between the features and the class label. This ensures that the imputation of the training data is directed towards improving classification performance. This class weighted grey kNN imputation algorithm demonstrates improved performance when compared to other kNN imputation algorithms, as well as standard imputation algorithms such as MICE and missForest, in imputation and classification problems. These problems are based on simulated scenarios and UCI datasets with various rates of missingness.

Methods for taking into account external knowledge in Machine Learning models have the potential to address outstanding issues in data-driven AI methods, such as improving safety and fairness, and can simplify training in the presence of scarce data. We propose a simple, but effective, method for injecting constraints at training time in supervised learning, based on decomposition and bi-level optimization: a master step is in charge of enforcing the constraints, while a learner step takes care of training the model. The process leads to approximate constraint satisfaction. The method is applicable to any ML approach for which the concept of label (or target) is well defined (most regression and classification scenarios), and allows to reuse existing training algorithms with no modifications. We require no assumption on the constraints, although their properties affect the shape and complexity of the master problem. Convergence guarantees are hard to provide, but we found that the approach performs well on ML tasks with fairness constraints and on classical datasets with synthetic constraints.

In the previous article, we studied Artificial Intelligence, its functions, and its python implementations. In this article, we will be studying Machine Learning. One thing that I believe is that if we are able to correlate anything with us or our life, there are greater chances of understanding the concept. So I will try to explain everything by relating it to humans.

Accurate predictions of reactive mixing are critical for many Earth and environmental science problems. To investigate mixing dynamics over time under different scenarios, a high-fidelity, finite-element-based numerical model is built to solve the fast, irreversible bimolecular reaction-diffusion equations to simulate a range of reactive-mixing scenarios. A total of 2,315 simulations are performed using different sets of model input parameters comprising various spatial scales of vortex structures in the velocity field, time-scales associated with velocity oscillations, the perturbation parameter for the vortex-based velocity, anisotropic dispersion contrast, and molecular diffusion. Outputs comprise concentration profiles of the reactants and products. The inputs and outputs of these simulations are concatenated into feature and label matrices, respectively, to train 20 different machine learning (ML) emulators to approximate system behavior. The 20 ML emulators based on linear methods, Bayesian methods, ensemble learning methods, and multilayer perceptron (MLP), are compared to assess these models. The ML emulators are specifically trained to classify the state of mixing and predict three quantities of interest (QoIs) characterizing species production, decay, and degree of mixing. Linear classifiers and regressors fail to reproduce the QoIs; however, ensemble methods (classifiers and regressors) and the MLP accurately classify the state of reactive mixing and the QoIs. Among ensemble methods, random forest and decision-tree-based AdaBoost faithfully predict the QoIs. At run time, trained ML emulators are $\approx10^5$ times faster than the high-fidelity numerical simulations. Speed and accuracy of the ensemble and MLP models facilitate uncertainty quantification, which usually requires 1,000s of model run, to estimate the uncertainty bounds on the QoIs.

You might have heard about random forests as a somewhat-new analytical method in forestry. But how do they work?

In order to train the machine learning algorithms, researchers gathered data on patients from the Indiana Network for Patient Care. The models used information on prescriptions and diagnoses, which are structured fields, as well as medical notes, which are free text, to predict the onset of dementia. Researchers found that the free-text notes were the most valuable to help identify people at risk of developing the disease. The research team, which also included scientists from Georgia State, Albert Einstein College of Medicine and Solid Research Group, recently published its findings on two different machine learning approaches. The paper published in the Journal of the American Geriatrics Society analyzed the results of a natural language processing algorithm, which learns rules by analyzing examples, and the Artificial Intelligence in Medicine article shared the results from a random forest model, which is built using an ensemble of decision trees. Both methods showed similar accuracy at predicting the onset of dementia within one and three years of diagnosis.

Depression is a common mental disorder worldwide which causes a range of serious outcomes. The diagnosis of depression relies on patient-reported scales and psychiatrist interview which may lead to subjective bias. In recent years, more and more researchers are devoted to depression recognition in speech , which may be an effective and objective indicator. This study proposes a new speech segment fusion method based on decision tree to improve the depression recognition accuracy and conducts a validation on a sample of 52 subjects (23 depressed patients and 29 healthy controls). The recognition accuracy are 75.8% and 68.5% for male and female respectively on gender-dependent models. It can be concluded from the data that the proposed decision tree model can improve the depression classification performance.