Here we present DIVE: Data-driven Inference of Vertexwise Evolution. DIVE is an image-based disease progression model with single-vertex resolution, designed to reconstruct long-term patterns of brain pathology from short-term longitudinal data sets. DIVE clusters vertex-wise biomarker measurements on the cortical surface that have similar temporal dynamics across a patient population, and concurrently estimates an average trajectory of vertex measurements in each cluster. DIVE uniquely outputs a parcellation of the cortex into areas with common progression patterns, leading to a new signature for individual diseases. DIVE further estimates the disease stage and progression speed for every visit of every subject, potentially enhancing stratification for clinical trials or management. On simulated data, DIVE can recover ground truth clusters and their underlying trajectory, provided the average trajectories are sufficiently different between clusters. We demonstrate DIVE on data from two cohorts: the Alzheimer's Disease Neuroimaging Initiative (ADNI) and the Dementia Research Centre (DRC), UK, containing patients with Posterior Cortical Atrophy (PCA) as well as typical Alzheimer's disease (tAD). DIVE finds similar spatial patterns of atrophy for tAD subjects in the two independent datasets (ADNI and DRC), and further reveals distinct patterns of pathology in different diseases (tAD vs PCA) and for distinct types of biomarker data: cortical thickness from Magnetic Resonance Imaging (MRI) vs amyloid load from Positron Emission Tomography (PET). Finally, DIVE can be used to estimate a fine-grained spatial distribution of pathology in the brain using any kind of voxelwise or vertexwise measures including Jacobian compression maps, fractional anisotropy (FA) maps from diffusion imaging or other PET measures. DIVE source code is available online: https://github.com/mrazvan22/dive

We study the problem of generating adversarial examples in a black-box setting in which only loss-oracle access to a model is available. We introduce a framework that conceptually unifies much of the existing work on black-box attacks, and we demonstrate that the current state-of-the-art methods are optimal in a natural sense. Despite this optimality, we show how to improve black-box attacks by bringing a new element into the problem: gradient priors. We give a bandit optimization-based algorithm that allows us to seamlessly integrate any such priors, and we explicitly identify and incorporate two examples. The resulting methods use two to four times fewer queries and fail two to five times less often than the current state-of-the-art.

We propose a deep generative Markov State Model (DeepGenMSM) learning framework for inference of metastable dynamical systems and prediction of trajectories. After unsupervised training on time series data, the model contains (i) a probabilistic encoder that maps from high-dimensional configuration space to a small-sized vector indicating the membership to metastable (long-lived) states, (ii) a Markov chain that governs the transitions between metastable states and facilitates analysis of the long-time dynamics, and (iii) a generative part that samples the conditional distribution of configurations in the next time step. The model can be operated in a recursive fashion to generate trajectories to predict the system evolution from a defined starting state and propose new configurations. The DeepGenMSM is demonstrated to provide accurate estimates of the long-time kinetics and generate valid distributions for molecular dynamics (MD) benchmark systems. Remarkably, we show that DeepGenMSMs are able to make long time-steps in molecular configuration space and generate physically realistic structures in regions that were not seen in training data.

The representation of the posterior is a critical aspect of effective variational autoencoders (VAEs). Poor choices for the posterior have a detrimental impact on the generative performance of VAEs due to the mismatch with the true posterior. We extend the class of posterior models that may be learned by using undirected graphical models. We develop an efficient method to train undirected posteriors by showing that the gradient of the training objective with respect to the parameters of the undirected posterior can be computed by backpropagation through Markov chain Monte Carlo updates. We apply these gradient estimators for training discrete VAEs with Boltzmann machine posteriors and demonstrate that undirected models outperform previous results obtained using directed graphical models as posteriors.

Due to the phenomenon of "posterior collapse," current latent variable generative models pose a challenging design choice that either weakens the capacity of the decoder or requires augmenting the objective so it does not only maximize the likelihood of the data. In this paper, we propose an alternative that utilizes the most powerful generative models as decoders, whilst optimising the variational lower bound all while ensuring that the latent variables preserve and encode useful information. Our proposed $\delta$-VAEs achieve this by constraining the variational family for the posterior to have a minimum distance to the prior. For sequential latent variable models, our approach resembles the classic representation learning approach of slow feature analysis. We demonstrate the efficacy of our approach at modeling text on LM1B and modeling images: learning representations, improving sample quality, and achieving state of the art log-likelihood on CIFAR-10 and ImageNet $32\times 32$.

Bayesian optimization (BO) based on Gaussian process models is a powerful paradigm to optimize black-box functions that are expensive to evaluate. While several BO algorithms provably converge to the global optimum of the unknown function, they assume that the hyperparameters of the kernel are known in advance. This is not the case in practice and misspecification often causes these algorithms to converge to poor local optima. In this paper, we present the first BO algorithm that is provably no-regret and converges to the optimum without knowledge of the hyperparameters. We slowly adapt the hyperparameters of stationary kernels and thereby expand the associated function class over time, so that the BO algorithm considers more complex function candidates. Based on the theoretical insights, we propose several practical algorithms that achieve the empirical data efficiency of BO with online hyperparameter estimation, but retain theoretical convergence guarantees. We evaluate our method on several benchmark problems.

This paper presents a methodology and numerical algorithms for constructing accelerated gradient flows on the space of probability distributions. In particular, we extend the recent variational formulation of accelerated gradient methods in (wibisono, et. al. 2016) from vector valued variables to probability distributions. The variational problem is modeled as a mean-field optimal control problem. The maximum principle of optimal control theory is used to derive Hamilton's equations for the optimal gradient flow. The Hamilton's equation are shown to achieve the accelerated form of density transport from any initial probability distribution to a target probability distribution. A quantitative estimate on the asymptotic convergence rate is provided based on a Lyapunov function construction, when the objective functional is displacement convex. Two numerical approximations are presented to implement the Hamilton's equations as a system of $N$ interacting particles. The continuous limit of the Nesterov's algorithm is shown to be a special case with $N=1$. The algorithm is illustrated with numerical examples.

The event-driven and elastic nature of serverless runtimes makes them a very efficient and cost-effective alternative for scaling up computations. So far, they have mostly been used for stateless, data parallel and ephemeral computations. In this work, we propose using serverless runtimes to solve generic, large-scale optimization problems. Specifically, we build a master-worker setup using AWS Lambda as the source of our workers, implement a parallel optimization algorithm to solve a regularized logistic regression problem, and show that relative speedups up to 256 workers and efficiencies above 70% up to 64 workers can be expected. We also identify possible algorithmic and system-level bottlenecks, propose improvements, and discuss the limitations and challenges in realizing these improvements.

This paper presents an approach for constrained Gaussian Process (GP) regression where we assume that a set of linear transformations of the process are bounded. It is motivated by machine learning applications for high-consequence engineering systems, where this kind of information is often made available from phenomenological knowledge, and the resulting constraints may be essential to achieve the level of confidence needed. We consider a GP $f$ over functions on $\mathcal{X} \subset \mathbb{R}^{n}$ taking values in $\mathbb{R}$, where the process $\mathcal{L}f$ is still Gaussian when $\mathcal{L}$ is a linear operator. Our goal is to model $f$ under the constraint that realizations of $\mathcal{L}f$ are confined to a convex set of functions. In particular we require that $a \leq \mathcal{L}f \leq b$ given two functions $a$ and $b$ where $a < b$ pointwise. This formulation provides a consistent way of encoding multiple linear constraints, such as shape-constraints based on e.g. boundedness, monotonicity or convexity as a relevant example. We adopt the approach of using a sufficiently dense set of virtual observation locations where the constraint is required to hold, and derive the exact posterior for a conjugate likelihood. The results needed for stable numerical implementation are derived, together with an efficient sampling scheme for estimating the posterior process which is exact in the limit. A few numerical examples focusing on noiseless observations are given. This is relevant for computer code emulation and is also more computationally demanding than the alternative scenario with i.i.d. Gaussian noise.

This paper introduces a novel, generic active learning method for one-class classification. Active learning methods play an important role to reduce the efforts of manual labeling in the field of machine learning. Although many active learning approaches have been proposed during the last years, most of them are restricted on binary or multi-class problems. One-class classifiers use samples from only one class, the so-called target class, during training and hence require special active learning strategies. The few strategies proposed for one-class classification either suffer from their limitation on specific one-class classifiers or their performance depends on particular assumptions about datasets like imbalance. Our proposed method bases on using two one-class classifiers, one for the desired target class and one for the so-called outlier class. It allows to invent new query strategies, to use binary query strategies and to define simple stopping criteria. Based on the new method, two query strategies are proposed. The provided experiments compare the proposed approach with known strategies on various datasets and show improved results in almost all situations.