The use of episodic memories in continual learning has been shown to be effective in terms of alleviating catastrophic forgetting. In recent studies, several gradientbased approaches have been developed to make more efficient use of compact episodic memories, which constrain the gradients resulting from new samples with those from memorized samples, aiming to reduce the diversity of gradients from different tasks. In this paper, we reveal the relation between diversity of gradients and discriminativeness of representations, demonstrating connections between Deep Metric Learning and continual learning. Based on these findings, we propose a simple yet highly efficient method - Discriminative Representation Loss (DRL) - for continual learning. In comparison with several state-of-theart methods, DRL shows effectiveness with low computational cost on multiple benchmark experiments in the setting of online continual learning. In the real world, we are often faced with situations where data distributions are changing over time, and we would like to update our models by new data in time, with bounded growth in system size. These situations fall under the umbrella of "continual learning", which has many practical applications, such as recommender systems, retail supply chain optimization, and robotics (Lesort et al., 2019; Diethe et al., 2018; Tian et al., 2018).

Brittle optimization has been observed to adversely impact model likelihoods for regression and VAEs when simultaneously fitting neural network mappings from a (random) variable onto the mean and variance of a dependent Gaussian variable. Previous works have bolstered optimization and improved likelihoods, but fail other basic posterior predictive checks (PPCs). Under the PPC framework, we propose critiques to test predictive mean and variance calibration and the predictive distribution's ability to generate sensible data. We find that our attractively simple solution, to treat heteroscedastic variance variationally, sufficiently regularizes variance to pass these PPCs. We consider a diverse gamut of existing and novel priors and find our methods preserve or outperform existing model likelihoods while significantly improving parameter calibration and sample quality for regression and VAEs.

We study the cluster recovery problem in the semi-supervised active clustering framework. Given a finite set of input points, and an oracle revealing whether any two points lie in the same cluster, our goal is to recover all clusters exactly using as few queries as possible. To this end, we relax the spherical $k$-means cluster assumption of Ashtiani et al.\ to allow for arbitrary ellipsoidal clusters with margin. This removes the assumption that the clustering is center-based (i.e., defined through an optimization problem), and includes all those cases where spherical clusters are individually transformed by any combination of rotations, axis scalings, and point deletions. We show that, even in this much more general setting, it is still possible to recover the latent clustering exactly using a number of queries that scales only logarithmically with the number of input points. More precisely, we design an algorithm that, given $n$ points to be partitioned into $k$ clusters, uses $O(k^3 \ln k \ln n)$ oracle queries and $\tilde{O}(kn + k^3)$ time to recover the clustering with zero misclassification error. The $O(\cdot)$ notation hides an exponential dependence on the dimensionality of the clusters, which we show to be necessary thus characterizing the query complexity of the problem. Our algorithm is simple, easy to implement, and can also learn the clusters using low-stretch separators, a class of ellipsoids with additional theoretical guarantees. Experiments on large synthetic datasets confirm that we can reconstruct clusterings exactly and efficiently.

Diffusion maps is a manifold learning algorithm widely used for dimensionality reduction. Using a sample from a distribution, it approximates the eigenvalues and eigenfunctions of associated Laplace-Beltrami operators. Theoretical bounds on the approximation error are however generally much weaker than the rates that are seen in practice. This paper uses new approaches to improve the error bounds in the model case where the distribution is supported on a hypertorus. For the data sampling (variance) component of the error we make spatially localised compact embedding estimates on certain Hardy spaces; we study the deterministic (bias) component as a perturbation of the Laplace-Beltrami operator's associated PDE, and apply relevant spectral stability results. Using these approaches, we match long-standing pointwise error bounds for both the spectral data and the norm convergence of the operator discretisation. We also introduce an alternative normalisation for diffusion maps based on Sinkhorn weights. This normalisation approximates a Langevin diffusion on the sample and yields a symmetric operator approximation. We prove that it has better convergence compared with the standard normalisation on flat domains, and present a highly efficient algorithm to compute the Sinkhorn weights.

This is an edited version of my undergraduate thesis, submitted to the Harvard Mathematics Department in May 2020. It differs from the original thesis in one major respect, namely that this version omits the proofs of a number of theorems that are readily-available in other expositions. Whereas the original version reproduced these proofs in full, this version simply contains references to these proofs in other works. This thesis is built upon an extensive body of prior work in learning theory, graph theory, differential geometry, and manifold learning. In particular, I would like to thank Professors Lorenzo Rosasco and Tomaso Poggio for their lectures on statistical learning theory, Professor Daniel Spielman for his notes on spectral graph theory, Professor Yaiza Canzani for her notes on analysis on manifolds, and Professor Mikhail Belkin for his work on manifold learning. Finally, I wish to thank those people without whom I could never have written this thesis: my family, friends, and wonderful advisor Professor Arjun Manrai. Unlike the manifolds discussed herein, their support was truly boundless. I hope you enjoy and learn something from this thesis! If you have comments, corrections, or would like to contact me for anything else, feel free to email me.

In this paper, we study efficient differentially private alternating direction methods of multipliers (ADMM) via gradient perturbation for many machine learning problems. For smooth convex loss functions with (non)-smooth regularization, we propose the first differentially private ADMM (DP-ADMM) algorithm with performance guarantee of $(\epsilon,\delta)$-differential privacy ($(\epsilon,\delta)$-DP). From the viewpoint of theoretical analysis, we use the Gaussian mechanism and the conversion relationship between R\'enyi Differential Privacy (RDP) and DP to perform a comprehensive privacy analysis for our algorithm. Then we establish a new criterion to prove the convergence of the proposed algorithms including DP-ADMM. We also give the utility analysis of our DP-ADMM. Moreover, we propose an accelerated DP-ADMM (DP-AccADMM) with the Nesterov's acceleration technique. Finally, we conduct numerical experiments on many real-world datasets to show the privacy-utility tradeoff of the two proposed algorithms, and all the comparative analysis shows that DP-AccADMM converges faster and has a better utility than DP-ADMM, when the privacy budget $\epsilon$ is larger than a threshold.

We live in a world where an increasing number of decisions, with major societal consequences, are made or at least supported by algorithms that diligently learn the patterns from a training sample and gain their discriminating ability by identifying the key attributes correlated with the desired output. These attributes, however, can represent sensitive information that, in its turn, can lead to a significant bias in model's predictions when deployed on a previously unseen sample. For instance, when building a recommendation system supporting a recruitment company in finding a potential candidate suitable for their clients' needs, one would expect its recommendations to be independent from the gender or the ethnicity of the considered individuals. In practice, however, the training sample used to learn the model may have been collected in a biased manner with an unequal number of successive outcomes between the genders and/or ethnic groups. The recommendations of the learned model in this case will tend to follow the learned pattern thus reinforcing the already existent bias. Research works aiming at identifying and correcting such inductive bias form the core of the algorithmic fairness field, a scientific area that is constantly gaining more and more attention from the machine learning and data mining communities nowadays. Algorithmic fairness methods are traditionally divided into one of the three following categories: (i) pre-processing methods that repair the original data to remove the bias, ii) methods that integrate fairness constraints or penalties in a given learning algorithm and iii) post-processing methods that debias directly the model's output. First family of methods can be further divided into two subfamilies where the first one corrects the input raw data to ensure that the inference of the sensitive attribute is impossible, regardless of the learning algorithm (e.g.

Clinical decision making about treatments and interventions based on personal characteristics leads to effective health improvement. Machine learning (ML) has been the central concern of the diagnosis support and disease prediction based on comprehensive patient information. Because the black-box problem in ML is serious for medical applications, explainable artificial intelligence (XAI) techniques to explain the reasons for ML models predictions have been focused. A remaining important issue in clinical situations is discovery of concrete and realistic treatment processes. This paper proposes an innovative framework to plan concrete treatment processes based on an ML model. A key point of our proposed framework is to evaluate an "actionability" of the treatment process using a stochastic surrogate model constructed through hierarchical Bayesian modeling. The actionability is an essential concept for suggesting a realistic treatment process, which leads to clinical applications for personal health improvement. This paper also presents two experiments to evaluate our framework. We first demonstrate the feasibility of our framework from the viewpoint of the methodology using a synthetic dataset. Subsequently, our framework is applied to an actual health checkup dataset, which comprises 3,132 participants, considering an application to improve systolic blood pressure values at a personal level. We confirmed that the computed treatment processes are actionable and consistent with clinical knowledge for lowering blood pressure. These results demonstrate that our framework can contribute to decision making in the medical field. Our framework can be expected to provide clinicians deeper insights by proposing concrete and actionable treatment process based on the ML model.

In this blog post, I will explain how machine learning fits into the broader landscape of data and computer science. This means understanding how machine learning interrelates with parent fields and sister disciplines. This is important, as these are the terms you will see time and again when searching for relevant study materials and hear mentioned ad nauseam in machine learning books. Relevant disciplines can also be difficult and confusing to tell apart at first glance, such as'machine learning' and'data mining.' The lineage of machine learning can be understood by first examining its forefathers.

In the previous article here, we have gone through the different methods to deal with imbalanced data. In this article, let us try to understand how to use imbalanced-learn library to deal with imbalanced class problems. We will make use of Pycaret library and UCI's default of credit card client dataset which is also in-built into PyCaret. Imbalanced-learn is a python package that provides a number of re-sampling techniques to deal with class imbalance problems commonly encountered in classification tasks. Note that imbalanced-learn is compatible with scikit-learn and is also part of scikit-learn-contrib projects.