In sequential machine teaching, a teacher's objective is to provide the optimal sequence of inputs to sequential learners in order to guide them towards the best model. In this paper we extend this setting from current static one-data-set analyses to learners which change their learning algorithm or latent state to improve during learning, and to generalize to new datasets. We introduce a multi-agent formulation in which learners' inner state may change with the teaching interaction, which affects the learning performance in future tasks. In order to teach such learners, we propose an optimal control approach that takes the future performance of the learner after teaching into account. This provides tools for modelling learners having inner states, and machine teaching of meta-learning algorithms. Furthermore, we distinguish manipulative teaching, which can be done by effectively hiding data and also used for indoctrination, from more general education which aims to help the learner become better at generalization and learning in new datasets in the absence of a teacher.

With the success of big data and artificial intelligence in many fields, the applications of big data driven models are expected in financial risk management especially credit scoring and rating. Under the premise of data privacy protection, we propose a projected gradient-based method in the vertical federated learning framework for the traditional scorecard, which is based on logistic regression with bounded constraints, namely FL-LRBC. The latter enables multiple agencies to jointly train an optimized scorecard model in a single training session. It leads to the formation of the model with positive coefficients, while the time-consuming parameter-tuning process can be avoided. Moreover, the performance in terms of both AUC and the Kolmogorov-Smirnov (KS) statistics is significantly improved due to data enrichment using FL-LRBC. At present, FL-LRBC has already been applied to credit business in a China nation-wide financial holdings group.

Fairness in machine learning has received considerable attention. However, most studies on fair learning focus on either supervised learning or unsupervised learning. Very few consider semi-supervised settings. Yet, in reality, most machine learning tasks rely on large datasets that contain both labeled and unlabeled data. One of key issues with fair learning is the balance between fairness and accuracy. Previous studies arguing that increasing the size of the training set can have a better trade-off. We believe that increasing the training set with unlabeled data may achieve the similar result. Hence, we develop a framework for fair semi-supervised learning, which is formulated as an optimization problem. This includes classifier loss to optimize accuracy, label propagation loss to optimize unlabled data prediction, and fairness constraints over labeled and unlabeled data to optimize the fairness level. The framework is conducted in logistic regression and support vector machines under the fairness metrics of disparate impact and disparate mistreatment. We theoretically analyze the source of discrimination in semi-supervised learning via bias, variance and noise decomposition. Extensive experiments show that our method is able to achieve fair semi-supervised learning, and reach a better trade-off between accuracy and fairness than fair supervised learning.

It is notoriously hard to build a bad Random Forest (RF). Concurrently, RF is perhaps the only standard ML algorithm that blatantly overfits in-sample without any consequence out-of-sample. Standard arguments cannot rationalize this paradox. I propose a new explanation: bootstrap aggregation and model perturbation as implemented by RF automatically prune a (latent) true underlying tree. More generally, there is no need to tune the stopping point of a properly randomized ensemble of greedily optimized base learners. Thus, Boosting and MARS are eligible for automatic (implicit) tuning. I empirically demonstrate the property, with simulated and real data, by reporting that these new completely overfitting ensembles yield an out-of-sample performance equivalent to that of their tuned counterparts -- or better.

We aim to construct a class of learning algorithms that are of practical value to applied researchers in fields such as biostatistics, epidemiology and econometrics, where the need to learn from incompletely observed information is ubiquitous. To do so, we propose a new framework for statistical machine learning, which we call 'IF-learning' due to its reliance on influence functions (IFs). To characterise the fundamental limits of what is achievable within this framework, we need to enable semiparametric estimation and inference on structural target parameters that are functions of continuous inputs arising as identifiable functionals from statistical models. Therefore, we introduce a pointwise IF to replace the true IF when it does not exist and propose learning its uncentered pointwise expected value from data. This allows us to give provable guarantees, leveraging existing general results from statistics. Our framework is problem- and model-agnostic and can be used to estimate a broad variety of target parameters of interest in applied statistics: we can consider any target function for which an IF of a population-averaged version exists in analytic form. Throughout, we put particular focus on so-called coarsening at random/doubly robust problems with partially unobserved information. This includes problems such as treatment effect estimation and inference in the presence of missing outcome data. Within this framework, we then propose two general learning algorithms that leverage ideas from the theoretical analysis: the 'IF-learner' which relies on large samples and outputs entire target functions without confidence bands, and the 'Group-IF-learner', which outputs only approximations to a function but can give confidence estimates if sufficient information on coarsening mechanisms is available. We close with a simulation study on inferring treatment effects.

Many existing tools in nonlinear control theory for establishing stability or safety of a dynamical system can be distilled to the construction of a certificate function that guarantees a desired property. However, algorithms for synthesizing certificate functions typically require a closed-form analytical expression of the underlying dynamics, which rules out their use on many modern robotic platforms. To circumvent this issue, we develop algorithms for learning certificate functions only from trajectory data. We establish bounds on the generalization error - the probability that a certificate will not certify a new, unseen trajectory - when learning from trajectories, and we convert such generalization error bounds into global stability guarantees. We demonstrate empirically that certificates for complex dynamics can be efficiently learned, and that the learned certificates can be used for downstream tasks such as adaptive control.

We introduce the I-prior methodology as a unifying framework for estimating a variety of regression models, including varying coefficient, multilevel, longitudinal models, and models with functional covariates and responses. It can also be used for multi-class classification, with low or high dimensional covariates. The I-prior is generally defined as a maximum entropy prior. For a regression function, the I-prior is Gaussian with covariance kernel proportional to the Fisher information on the regression function, which is estimated by its posterior distribution under the I-prior. The I-prior has the intuitively appealing property that the more information is available on a linear functional of the regression function, the larger the prior variance, and the smaller the influence of the prior mean on the posterior distribution. Advantages compared to competing methods, such as Gaussian process regression or Tikhonov regularization, are ease of estimation and model comparison. In particular, we develop an EM algorithm with a simple E and M step for estimating hyperparameters, facilitating estimation for complex models. We also propose a novel parsimonious model formulation, requiring a single scale parameter for each (possibly multidimensional) covariate and no further parameters for interaction effects. This simplifies estimation because fewer hyperparameters need to be estimated, and also simplifies model comparison of models with the same covariates but different interaction effects; in this case, the model with the highest estimated likelihood can be selected. Using a number of widely analyzed real data sets we show that predictive performance of our methodology is competitive. An R-package implementing the methodology is available (Jamil, 2019).

The use of quadratic discriminant analysis (QDA) or its regularized version (R-QDA) for classification is often not recommended, due to its well-acknowledged high sensitivity to the estimation noise of the covariance matrix. This becomes all the more the case in unbalanced data settings for which it has been found that R-QDA becomes equivalent to the classifier that assigns all observations to the same class. In this paper, we propose an improved R-QDA that is based on the use of two regularization parameters and a modified bias, properly chosen to avoid inappropriate behaviors of R-QDA in unbalanced settings and to ensure the best possible classification performance. The design of the proposed classifier builds on a refined asymptotic analysis of its performance when the number of samples and that of features grow large simultaneously, which allows to cope efficiently with the high-dimensionality frequently met within the big data paradigm. The performance of the proposed classifier is assessed on both real and synthetic data sets and was shown to be much better than what one would expect from a traditional R-QDA.

Cardiovascular Disease (CVD) is an important cause of disability and death among individuals with Diabetes Mellitus (DM). International clinical guidelines for the management of Type 2 DM (T2DM) are founded on primary and secondary prevention and favor the evaluation of CVD related risk factors towards appropriate treatment initiation. CVD risk prediction models can provide valuable tools for optimizing the frequency of medical visits and performing timely preventive and therapeutic interventions against CVD events. The integration of explainability modalities in these models can enhance human understanding on the reasoning process, maximize transparency and embellish trust towards the models' adoption in clinical practice. The aim of the present study is to develop and evaluate an explainable personalized risk prediction model for the fatal or non-fatal CVD incidence in T2DM individuals. An explainable approach based on the eXtreme Gradient Boosting (XGBoost) and the Tree SHAP (SHapley Additive exPlanations) method is deployed for the calculation of the 5-year CVD risk and the generation of individual explanations on the model's decisions. Data from the 5-year follow up of 560 patients with T2DM are used for development and evaluation purposes. The obtained results (AUC = 71.13%) indicate the potential of the proposed approach to handle the unbalanced nature of the used dataset, while providing clinically meaningful insights about the ensemble model's decision process.

I'm currently going through the textbook Introduction to Machine Learning 4e (Ethem Alpaydin) to brush up on my ML basics and had a question regarding the chapter on multivariate methods. More