We study the Extended Kalman Filter in constant dynamics, offering a bayesian perspective of stochastic optimization. We obtain high probability bounds on the cumulative excess risk in an unconstrained setting. In order to avoid any projection step we propose a two-phase analysis. First, for linear and logistic regressions, we prove that the algorithm enters a local phase where the estimate stays in a small region around the optimum. We provide explicit bounds with high probability on this convergence time. Second, for generalized linear regressions, we provide a martingale analysis of the excess risk in the local phase, improving existing ones in bounded stochastic optimization. The EKF appears as a parameter-free online algorithm with O(d^2) cost per iteration that optimally solves some unconstrained optimization problems.

For example, NCF [8] takes user-item implicit feedback data as inputs for the rating prediction task; and DeepFM [6] leverages both numerical and categorical data for the CTR prediction task. However, high degree of specialization comes at the expense of model adaptability and tuning complexity. As recommendation tasks evolve over time and additional types of data are collected, the originally apt model can either become obsolete or require tremendous tuning efforts. So far, several pipelines for recommender systems, e.g., OpenRec [16] and SMORe [4], tried to address the adaptability issue via providing modular base blocks that can be selected according to the context of recommendation. Nevertheless, both determining the blocks to use and tuning the model parameters are not straightforward when facing new data and changing tasks. In order to bridge the gap, we present AutoRec, which aims to provide an end-to-end solution to automate model selection and hyperparameter tuning. While many AutoML libraries, such as Auto-Sklearn [5] and TPOT [12] have shown promising results in general-purpose machine learning tasks (e.g., regression and hyperparameter tuning) and

Many contemporary applications in signal processing and machine learning give rise to structured non-convex non-smooth optimization problems that can often be tackled by simple iterative methods quite effectively. One of the keys to understanding such a phenomenon---and, in fact, one of the very difficult conundrums even for experts---lie in the study of "stationary points" of the problem in question. Unlike smooth optimization, for which the definition of a stationary point is rather standard, there is a myriad of definitions of stationarity in non-smooth optimization. In this article, we give an introduction to different stationarity concepts for several important classes of non-convex non-smooth functions and discuss the geometric interpretations and further clarify the relationship among these different concepts. We then demonstrate the relevance of these constructions in some representative applications and how they could affect the performance of iterative methods for tackling these applications.

We consider the problem of learning a sparse graph under Laplacian constrained Gaussian graphical models. This problem can be formulated as a penalized maximum likelihood estimation of the precision matrix under Laplacian structural constraints. Like in the classical graphical lasso problem, recent works made use of the $\ell_1$-norm regularization with the goal of promoting sparsity in Laplacian structural precision matrix estimation. However, we find that the widely used $\ell_1$-norm is not effective in imposing a sparse solution in this problem. Through empirical evidence, we observe that the number of nonzero graph weights grows with the increase of the regularization parameter. From a theoretical perspective, we prove that a large regularization parameter will surprisingly lead to a fully connected graph. To address this issue, we propose a nonconvex estimation method by solving a sequence of weighted $\ell_1$-norm penalized sub-problems and prove that the statistical error of the proposed estimator matches the minimax lower bound. To solve each sub-problem, we develop a projected gradient descent algorithm that enjoys a linear convergence rate. Numerical experiments involving synthetic and real-world data sets from the recent COVID-19 pandemic and financial stock markets demonstrate the effectiveness of the proposed method. An open source $\mathsf{R}$ package containing the code for all the experiments is available at https://github.com/mirca/sparseGraph.

It has long been argued that minibatch stochastic gradient descent can generalize better than large batch gradient descent in deep neural networks. However recent papers have questioned this claim, arguing that this effect is simply a consequence of suboptimal hyperparameter tuning or insufficient compute budgets when the batch size is large. In this paper, we perform carefully designed experiments and rigorous hyperparameter sweeps on a range of popular models, which verify that small or moderately large batch sizes can substantially outperform very large batches on the test set. This occurs even when both models are trained for the same number of iterations and large batches achieve smaller training losses. Our results confirm that the noise in stochastic gradients can enhance generalization. We study how the optimal learning rate schedule changes as the epoch budget grows, and we provide a theoretical account of our observations based on the stochastic differential equation perspective of SGD dynamics.

Deep Neural Networks are well known to be vulnerable to adversarial attacks and backdoor attacks, where minor modifications on the input can mislead the models to give wrong results. Although defenses against adversarial attacks have been widely studied, research on mitigating backdoor attacks is still at an early stage. It is unknown whether there are any connections and common characteristics between the defenses against these two attacks. In this paper, we present a unified framework for detecting malicious examples and protecting the inference results of Deep Learning models. This framework is based on our observation that both adversarial examples and backdoor examples have anomalies during the inference process, highly distinguishable from benign samples. As a result, we repurpose and revise four existing adversarial defense methods for detecting backdoor examples. Extensive evaluations indicate these approaches provide reliable protection against backdoor attacks, with a higher accuracy than detecting adversarial examples. These solutions also reveal the relations of adversarial examples, backdoor examples and normal samples in model sensitivity, activation space and feature space. This can enhance our understanding about the inherent features of these two attacks, as well as the defense opportunities.

The two main challenges faced by continual learning approaches are catastrophic forgetting and memory limitations on the storage of data. To cope with these challenges, we propose a novel, cognitively-inspired approach which trains autoencoders with Neural Style Transfer to encode and store images. Reconstructed images from encoded episodes are replayed when training the classifier model on a new task to avoid catastrophic forgetting. The loss function for the reconstructed images is weighted to reduce its effect during classifier training to cope with image degradation. When the system runs out of memory the encoded episodes are converted into centroids and covariance matrices, which are used to generate pseudo-images during classifier training, keeping classifier performance stable with less memory. Our approach increases classification accuracy by 13-17% over state-of-the-art methods on benchmark datasets, while requiring 78% less storage space.

A method for counterfactual explanation of machine learning survival models is proposed. One of the difficulties of solving the counterfactual explanation problem is that the classes of examples are implicitly defined through outcomes of a machine learning survival model in the form of survival functions. A condition that establishes the difference between survival functions of the original example and the counterfactual is introduced. This condition is based on using a distance between mean times to event. It is shown that the counterfactual explanation problem can be reduced to a standard convex optimization problem with linear constraints when the explained black-box model is the Cox model. For other black-box models, it is proposed to apply the well-known Particle Swarm Optimization algorithm. A lot of numerical experiments with real and synthetic data demonstrate the proposed method.

Machine learning methods applied to complex biomedical data has enabled the construction of disease signatures of diagnostic/prognostic value. However, less attention has been given to understanding disease heterogeneity. Semi-supervised clustering methods can address this problem by estimating multiple transformations from a (e.g. healthy) control (CN) group to a patient (PT) group, seeking to capture the heterogeneity of underlying pathlogic processes. Herein, we propose a novel method, Smile-GANs (SeMi-supervIsed cLustEring via GANs), for semi-supervised clustering, and apply it to brain MRI scans. Smile-GANs first learns multiple distinct mappings by generating PT from CN, with each mapping characterizing one relatively distinct pathological pattern. Moreover, a clustering model is trained interactively with mapping functions to assign PT into corresponding subtype memberships. Using relaxed assumptions on PT/CN data distribution and imposing mapping non-linearity, Smile-GANs captures heterogeneous differences in distribution between the CN and PT domains. We first validate Smile-GANs using simulated data, subsequently on real data, by demonstrating its potential in characterizing heterogeneity in Alzheimer's Disease (AD) and its prodromal phases. The model was first trained using baseline MRIs from the ADNI2 database and then applied to longitudinal data from ADNI1 and BLSA. Four robust subtypes with distinct neuroanatomical patterns were discovered: 1) normal brain, 2) diffuse atrophy atypical of AD, 3) focal medial temporal lobe atrophy, 4) typical-AD. Further longitudinal analyses discover two distinct progressive pathways from prodromal to full AD: i) subtypes 1 - 2 - 4, and ii) subtypes 1 - 3 - 4. Although demonstrated on an important biomedical problem, Smile-GANs is general and can find application in many biomedical and other domains.

It is often infeasible or impossible to obtain ground truth labels for medical data. To circumvent this, one may build rule-based or other expert-knowledge driven labelers to ingest data and yield silver labels absent any ground-truth training data. One popular such labeler is CheXpert (Irvin et al., 2019), a labeler that produces diagnostic labels for chest X-ray radiology reports. CheXpert is very useful, but is relatively computationally slow, especially when integrated with end-to-end neural pipelines, is non-differentiable so can't be used in any applications that require gradients to flow through the labeler, and does not yield probabilistic outputs, which limits our ability to improve the quality of the silver labeler through techniques such as active learning. In this work, we solve all three of these problems with CheXpert, a BERTbased, highfidelity approximation to CheXpert. CheXpert achieves 99.81% parity with CheXpert, which means it can be reliably used as a drop-in replacement for CheXpert, all while being significantly faster, fully differentiable, and probabilistic in output. Error analysis of CheXpert also demonstrates that CheXpert has a tendency to actually correct errors in the CheXpert labels, with CheXpert labels being more often preferred by a clinician over CheXpert labels (when they disagree) on all but one disease task. To further demonstrate the utility of these advantages in this model, we conduct a proof-of-concept active learning study, demonstrating we can improve accuracy on an expert labeled random subset of report sentences by approximately 8% over raw, unaltered CheXpert by using one-iteration of active-learning inspired retraining. These findings suggest that simple techniques in co-learning and active learning can yield high-quality labelers under minimal, and controllable human labeling demands.