Chemical autoencoders are attractive models as they combine chemical space navigation with possibilities for de novo molecule generation in areas of interest. This enables them to produce focused chemical libraries around a single lead compound so they can be employed early in a drug discovery project. Here it is shown that the choice of chemical representation, such as SMILES strings, has a large influence on the properties of the latent space. It is further explored to what extent translating between different chemical representations influences the latent space similarity to the SMILES strings or circular fingerprints. By employing SMILES enumeration for both the encoder and decoder, it is found that the decoder has the largest influence on the properties of the latent space. Training a sequence to sequence heteroencoder based on recurrent neural networks(RNNs) with long short-term memory cells (LSTM) to predicts different enumerated SMILES strings from the same canonical SMILES string gives the largest similarity between latent space distance and molecular similarity measured as circular fingerprints similarity.

Using stochastic gradient search and the optimal filter derivative, it is possible to perform recursive (i.e., online) maximum likelihood estimation in a non-linear state-space model. As the optimal filter and its derivative are analytically intractable for such a model, they need to be approximated numerically. In [Poyiadjis, Doucet and Singh, Biometrika 2018], a recursive maximum likelihood algorithm based on a particle approximation to the optimal filter derivative has been proposed and studied through numerical simulations. Here, this algorithm and its asymptotic behavior are analyzed theoretically. We show that the algorithm accurately estimates maxima to the underlying (average) log-likelihood when the number of particles is sufficiently large. We also derive (relatively) tight bounds on the estimation error. The obtained results hold under (relatively) mild conditions and cover several classes of non-linear state-space models met in practice.

As artificial intelligence is increasingly affecting all parts of society and life, there is growing recognition that human interpretability of machine learning models is important. It is often argued that accuracy or other similar generalization performance metrics must be sacrificed in order to gain interpretability. Such arguments, however, fail to acknowledge that the overall decision-making system is composed of two entities: the learned model and a human who fuses together model outputs with his or her own information. As such, the relevant performance criteria should be for the entire system, not just for the machine learning component. In this work, we characterize the performance of such two-node tandem data fusion systems using the theory of distributed detection. In doing so, we work in the population setting and model interpretable learned models as multi-level quantizers. We prove that under our abstraction, the overall system of a human with an interpretable classifier outperforms one with a black box classifier.

Many applications, including rank aggregation, crowd-labeling, and graphon estimation, can be modeled in terms of a bivariate isotonic matrix with unknown permutations acting on its rows and columns. We consider the problem of estimating such a matrix based on noisy observations of a subset of its entries, and design and analyze polynomial-time algorithms that improve upon the state of the art. In particular, our results imply that any such $n \times n$ matrix can be estimated efficiently in the normalized, squared Frobenius norm at rate $\widetilde{\mathcal O}(n^{-3/4})$, thus narrowing the gap between $\widetilde{\mathcal O}(n^{-1})$ and $\widetilde{\mathcal O}(n^{-1/2})$, hitherto the rates of the most statistically and computationally efficient methods, respectively. Additionally, our algorithms are minimax optimal in another natural metric that measures how well an estimate captures each row of the matrix. Along the way, we prove matching upper and lower bounds on the minimax radii of certain cone testing problems, which may be of independent interest.

Magnetic resonance (MR) imaging offers a wide variety of imaging techniques. A large amount of data is created per examination which needs to be checked for sufficient quality in order to derive a meaningful diagnosis. This is a manual process and therefore time- and cost-intensive. Any imaging artifacts originating from scanner hardware, signal processing or induced by the patient may reduce the image quality and complicate the diagnosis or any image post-processing. Therefore, the assessment or the ensurance of sufficient image quality in an automated manner is of high interest. Usually no reference image is available or difficult to define. Therefore, classical reference-based approaches are not applicable. Model observers mimicking the human observers (HO) can assist in this task. Thus, we propose a new machine-learning-based reference-free MR image quality assessment framework which is trained on HO-derived labels to assess MR image quality immediately after each acquisition. We include the concept of active learning and present an efficient blinded reading platform to reduce the effort in the HO labeling procedure. Derived image features and the applied classifiers (support-vector-machine, deep neural network) are investigated for a cohort of 250 patients. The MR image quality assessment framework can achieve a high test accuracy of 93.7$\%$ for estimating quality classes on a 5-point Likert-scale. The proposed MR image quality assessment framework is able to provide an accurate and efficient quality estimation which can be used as a prospective quality assurance including automatic acquisition adaptation or guided MR scanner operation, and/or as a retrospective quality assessment including support of diagnostic decisions or quality control in cohort studies.

Learning of dynamical systems, or state-space models, is central to many machine learning problems, such as reinforcement learning, sequence modeling, and autonomous systems. Furthermore, state-space models are at the core of recent model developments within the machine learning area, such as Gaussian process state-space models (Frigola et al. 2014a; Mattos et al. 2016; etc.), infinite factorial dynamical models (Gael et al., 2009; Valera et al., 2015), and stochastic recurrent neural networks (Fraccaro et al., 2016, for example). A strategy to learn state-space models, independently suggested by Digalakis et al. (1993) and Ghahramani and Hinton (1996), is the use of the Expectation Maximization (EM, Dempster et al. 1977) method. Even though originally proposed only for maximum likelihood estimation of linear models with Gaussian noise, the strategy can be generalized to the more challenging nonlinear and non-Gaussian cases, as well as the empirical Bayes setting. Many contributions have been made during the last decade, and this paper takes another step along the path towards a more computationally efficient method with a solid theoretical ground for learning of nonlinear dynamical systems.

We study the fundamental limits of detecting the presence of an additive rank-one perturbation, or spike, to a Wigner matrix. When the spike comes from a prior that is i.i.d. across coordinates, we prove that the log-likelihood ratio of the spiked model against the non-spiked one is asymptotically normal below a certain reconstruction threshold which is not necessarily of a "spectral" nature, and that it is degenerate above. This establishes the maximal region of contiguity between the planted and null models. It is known that this threshold also marks a phase transition for estimating the spike: the latter task is possible above the threshold and impossible below. Therefore, both estimation and detection undergo the same transition in this random matrix model. We also provide further information about the performance of the optimal test. Our proofs are based on Gaussian interpolation methods and a rigorous incarnation of the cavity method, as devised by Guerra and Talagrand in their study of the Sherrington--Kirkpatrick spin-glass model.

Pseudo-marginal Metropolis-Hastings (pmMH) is a versatile algorithm for sampling from target distributions which are not easy to evaluate point-wise. However, pmMH requires good proposal distributions to sample efficiently from the target, which can be problematic to construct in practice. This is especially a problem for high-dimensional targets when the standard random-walk proposal is inefficient. We extend pmMH to allow for constructing the proposal based on information from multiple past iterations. As a consequence, quasi-Newton (qN) methods can be employed to form proposals which utilize gradient information to guide the Markov chain to areas of high probability and to construct approximations of the local curvature to scale step sizes. The proposed method is demonstrated on several problems which indicate that qN proposals can perform better than other common Hessian-based proposals.

We study optimization methods for solving the maximum likelihood formulation of independent component analysis (ICA). We consider both the the problem constrained to white signals and the unconstrained problem. The Hessian of the objective function is costly to compute, which renders Newton's method impractical for large data sets. Many algorithms proposed in the literature can be rewritten as quasi-Newton methods, for which the Hessian approximation is cheap to compute. These algorithms are very fast on simulated data where the linear mixture assumption really holds. However, on real signals, we observe that their rate of convergence can be severely impaired. In this paper, we investigate the origins of this behavior, and show that the recently proposed Preconditioned ICA for Real Data (Picard) algorithm overcomes this issue on both constrained and unconstrained problems.

Given $n$ samples from a population of individuals belonging to different types with unknown proportions, how do we estimate the probability of discovering a new type at the $(n+1)$-th draw? This is a classical problem in statistics, commonly referred to as the missing mass estimation problem. Recent results by Ohannessian and Dahleh \citet{Oha12} and Mossel and Ohannessian \citet{Mos15} showed: i) the impossibility of estimating (learning) the missing mass without imposing further structural assumptions on the type proportions; ii) the consistency of the Good-Turing estimator for the missing mass under the assumption that the tail of the type proportions decays to zero as a regularly varying function with parameter $\alpha\in(0,1)$. In this paper we rely on tools from Bayesian nonparametrics to provide an alternative, and simpler, proof of the impossibility of a distribution-free estimation of the missing mass. Up to our knowledge, the use of Bayesian ideas to study large sample asymptotics for the missing mass is new, and it could be of independent interest. Still relying on Bayesian nonparametric tools, we then show that under regularly varying type proportions the convergence rate of the Good-Turing estimator is the best rate that any estimator can achieve, up to a slowly varying function, and that minimax rate must be at least $n^{-\alpha/2}$. We conclude with a discussion of our results, and by conjecturing that the Good-Turing estimator is an rate optimal minimax estimator under regularly varying type proportions.