Prediction of diabetes and its various complications has been studied in a number of settings, but a comprehensive overview of problem setting for diabetes prediction and care management has not been addressed in the literature. In this document we seek to remedy this omission in literature with an encompassing overview of diabetes complication prediction as well as situating this problem in the context of real world healthcare management. We illustrate various problems encountered in real world clinical scenarios via our own experience with building and deploying such models. In this manuscript we illustrate a Machine Learning (ML) framework for addressing the problem of predicting Type 2 Diabetes Mellitus (T2DM) together with a solution for risk stratification, intervention and management. These ML models align with how physicians think about disease management and mitigation, which comprises these four steps: Identify, Stratify, Engage, Measure.

Incrementally training deep neural networks to recognize new classes is a challenging problem. Most existing class-incremental learning methods store data or use generative replay, both of which have drawbacks, while 'rehearsal-free' alternatives such as parameter regularization or bias-correction methods do not consistently achieve high performance. Here, we put forward a new strategy for class-incremental learning: generative classification. Rather than directly learning the conditional distribution p(y|x), our proposal is to learn the joint distribution p(x,y), factorized as p(x|y)p(y), and to perform classification using Bayes' rule. As a proof-of-principle, here we implement this strategy by training a variational autoencoder for each class to be learned and by using importance sampling to estimate the likelihoods p(x|y). This simple approach performs very well on a diverse set of continual learning benchmarks, outperforming generative replay and other existing baselines that do not store data.

In every corner of machine learning and statistics, there is a need for estimators that work not just in an idealized model, but even when their assumptions are violated. Unfortunately, in high dimensions, being provably robust and being efficiently computable are often at odds with each other. We give the first efficient algorithm for estimating the parameters of a high-dimensional Gaussian that is able to tolerate a constant fraction of corruptions that is independent of the dimension. Prior to our work, all known estimators either needed time exponential in the dimension to compute or could tolerate only an inverse-polynomial fraction of corruptions. Not only does our algorithm bridge the gap between robustness and algorithms, but also it turns out to be highly practical in a variety of settings. Machine learning is filled with examples of estimators that work well in idealized settings but fail when their assumptions are violated. In fact, these are examples of a more general paradigm within statistics called maximum likelihood estimation: When we know the distribution comes from some parametric family, we choose the parameters that are the most likely to have generated the observed data. In 1922, Ronald Fisher12 formulated the maximum likelihood principle. It has many wonderful properties (under various technical conditions), such as converging to the true parameters as the number of samples goes to infinity, a property called consistency. Moreover, it has asymptotically the smallest possible variance among all unbiased estimators, a property called asymptotic consistency. In 1960, John Tukey24 challenged the conventional wisdom in parametric estimation by asking a simple question: Are there provably robust methods to estimate the parameters of a one-dimensional Gaussian?

High-dimensional limit theorems have been shown to be useful to derive tuning rules for finding the optimal scaling in random walk Metropolis algorithms. The assumptions under which weak convergence results are proved are however restrictive; the target density is typically assumed to be of a product form. Users may thus doubt the validity of such tuning rules in practical applications. In this paper, we shed some light on optimal scaling problems from a different perspective, namely a large-sample one. This allows to prove weak convergence results under realistic assumptions and to propose novel parameter-dimension-dependent tuning guidelines. The proposed guidelines are consistent with previous ones when the target density is close to having a product form, but significantly different otherwise.

In this paper, we take a human-centered approach to interpretable machine learning. First, drawing inspiration from the study of explanation in philosophy, cognitive science, and the social sciences, we propose a list of design principles for machine-generated explanations that are meaningful to humans. Using the concept of weight of evidence from information theory, we develop a method for producing explanations that adhere to these principles. We show that this method can be adapted to handle high-dimensional, multi-class settings, yielding a flexible meta-algorithm for generating explanations. We demonstrate that these explanations can be estimated accurately from finite samples and are robust to small perturbations of the inputs. We also evaluate our method through a qualitative user study with machine learning practitioners, where we observe that the resulting explanations are usable despite some participants struggling with background concepts like prior class probabilities. Finally, we conclude by surfacing design implications for interpretability tools

Due to the fact that basic uncertain information provides a simple form for decision information with certainty degree, it has been developed to reflect the quality of observed or subjective assessments. In order to study the algebra structure and preference relation of basic uncertain information, we develop some algebra operations for basic uncertain information. The order relation of such type of information has also been considered. Finally, to apply the developed algebra operations and order relations, a generalized TODIM method for multi-attribute decision making with basic uncertain information is given. The numerical example shows that the developed decision procedure is valid.

To minimize the average of a set of log-convex functions, the stochastic Newton method iteratively updates its estimate using subsampled versions of the full objective's gradient and Hessian. We contextualize this optimization problem as sequential Bayesian inference on a latent state-space model with a discriminatively-specified observation process. Applying Bayesian filtering then yields a novel optimization algorithm that considers the entire history of gradients and Hessians when forming an update. We establish matrix-based conditions under which the effect of older observations diminishes over time, in a manner analogous to Polyak's heavy ball momentum. We illustrate various aspects of our approach with an example and review other relevant innovations for the stochastic Newton method.

We present an application of invariant polynomials in machine learning. Using the methods developed in previous work, we obtain two types of generators of the Lorentz- and permutation-invariant polynomials in particle momenta; minimal algebra generators and Hironaka decompositions. We discuss and prove some approximation theorems to make use of these invariant generators in machine learning algorithms in general and in neural networks specifically. By implementing these generators in neural networks applied to regression tasks, we test the improvements in performance under a wide range of hyperparameter choices and find a reduction of the loss on training data and a significant reduction of the loss on validation data. For a different approach on quantifying the performance of these neural networks, we treat the problem from a Bayesian inference perspective and employ nested sampling techniques to perform model comparison. Beyond a certain network size, we find that networks utilising Hironaka decompositions perform the best.

Massive Open Online Courses (MOOCs) have become a popular choice for e-learning thanks to their great flexibility. However, due to large numbers of learners and their diverse backgrounds, it is taxing to offer real-time support. Learners may post their feelings of confusion and struggle in the respective MOOC forums, but with the large volume of posts and high workloads for MOOC instructors, it is unlikely that the instructors can identify all learners requiring intervention. This problem has been studied as a Natural Language Processing (NLP) problem recently, and is known to be challenging, due to the imbalance of the data and the complex nature of the task. In this paper, we explore for the first time Bayesian deep learning on learner-based text posts with two methods: Monte Carlo Dropout and Variational Inference, as a new solution to assessing the need of instructor interventions for a learner's post. We compare models based on our proposed methods with probabilistic modelling to its baseline non-Bayesian models under similar circumstances, for different cases of applying prediction. The results suggest that Bayesian deep learning offers a critical uncertainty measure that is not supplied by traditional neural networks. This adds more explainability, trust and robustness to AI, which is crucial in education-based applications. Additionally, it can achieve similar or better performance compared to non-probabilistic neural networks, as well as grant lower variance.

We study high-dimensional Bayesian linear regression with product priors. Using the nascent theory of non-linear large deviations (Chatterjee and Dembo,2016), we derive sufficient conditions for the leading-order correctness of the naive mean-field approximation to the log-normalizing constant of the posterior distribution. Subsequently, assuming a true linear model for the observed data, we derive a limiting infinite dimensional variational formula for the log normalizing constant of the posterior. Furthermore, we establish that under an additional "separation" condition, the variational problem has a unique optimizer, and this optimizer governs the probabilistic properties of the posterior distribution. We provide intuitive sufficient conditions for the validity of this "separation" condition. Finally, we illustrate our results on concrete examples with specific design matrices.