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Previous text-based depression detection is commonly based on large user-generated data. Sparse scenarios like clinical conversations are less investigated. This work proposes a text-based multi-task BGRU network with pretrained word embeddings to model patients' responses during clinical interviews. Our main approach uses a novel multi-task loss function, aiming at modeling both depression severity and binary health state. We independently investigate word- and sentence-level word-embeddings as well as the use of large-data pretraining for depression detection. To strengthen our findings, we report mean-averaged results for a multitude of independent runs on sparse data. First, we show that pretraining is helpful for word-level text-based depression detection. Second, our results demonstrate that sentence-level word-embeddings should be mostly preferred over word-level ones. While the choice of pooling function is less crucial, mean and attention pooling should be preferred over last-timestep pooling. Our method outputs depression presence results as well as predicted severity score, culminating a macro F1 score of 0.84 and MAE of 3.48 on the DAIC-WOZ development set.

SMC (Sequential Monte Carlo) is a class of Monte Carlo algorithms for filtering and related sequential problems. Gerber and Chopin (2015) introduced SQMC (Sequential quasi-Monte Carlo), a QMC version of SMC. This paper has two objectives: (a) to introduce Sequential Monte Carlo to the QMC community, whose members are usually less familiar with state-space models and particle filtering; (b) to extend SQMC to the filtering of continuous-time state-space models, where the latent process is a diffusion. A recurring point in the paper will be the notion of dimension reduction, that is how to implement SQMC in such a way that it provides good performance despite the high dimension of the problem. To be published in the proceedings of MCMQMC 2016

We compute the optical phase shifts between the left and the right-circularly polarized light after it traverses non-planar cyclic paths described by the boundary curves of closed twisted strips. The evolution of the electric field along the curved path of a light ray is described by the Fermi-Walker transport law which is mapped to a Schr��dinger equation. The effective quantum Hamiltonian of the system has eigenvalues equal to $0, \pm ��$, where $��$ is the local curvature of the path. The inflexion points of the twisted strips correspond to the vanishing of the curvature and manifest themselves as the diabolic crossings of the quantum Hamiltonian. For the M��bius loops, the critical width where the diabolic geometry resides also corresponds to the characteristic width where the optical phase shift is minimal. In our detailed study of various twisted strips, this intriguing property singles out the M"{o}bius geometry.

We consider the following elliptic system ��u =\nabla H (u) \ \ \text{in}\ \ \mathbf{R}^N, where $u:\mathbf{R}^N\to \mathbf{R}^m$ and $H\in C^2(\mathbf{R}^m)$, and prove, under various conditions on the nonlinearity $H$ that, at least in low dimensions, a solution $u=(u_i)_{i=1}^m$ is necessarily one-dimensional whenever each one of its components $u_i$ is monotone in one direction. Just like in the proofs of the classical De Giorgi's conjecture in dimension 2 (Ghoussoub-Gui) and in dimension 3 (Ambrosio-Cabr��), the key step is a Liouville theorem for linear systems. We also give an extension of a geometric Poincar�� inequality to systems and use it to establish De Giorgi type results for stable solutions as well as additional rigidity properties stating that the gradients of the various components of the solutions must be parallel. We introduce and exploit the concept of {\it an orientable system}, which seems to be key for dealing with systems of three or more equations. For such systems, the notion of a stable solution in a variational sense coincide with the pointwise (or spectral) concept of stability. 12 pages, improved on the earlier versions. Updated version - if any - can be downloaded at http://www.birs.ca/~nassif/

We consider an instationary macroscopic system of self-interacting particles with an additional potential, the so called Bohm's potential. We study the existence of non-negative global solutions to the (4-th order) system of equations and allude the differences to results obtained for classical models. The problem is considered on a bounded domain up to three space dimension, subject to initial and Neumann boundary condition for the particle density, and Dirichlet boundary condition for the self-interacting potential. Moreover, the initial datum is only assumed to be non-negative and to satisfy a weak integrability condition. 14 pages

In networking applications, one often wishes to obtain estimates about the number of objects at different parts of the network (e.g., the number of cars at an intersection of a road network or the number of packets expected to reach a node in a computer network) by monitoring the traffic in a small number of network nodes or edges. We formalize this task by defining the 'Markov Chain Monitoring' problem. Given an initial distribution of items over the nodes of a Markov chain, we wish to estimate the distribution of items at subsequent times. We do this by asking a limited number of queries that retrieve, for example, how many items transitioned to a specific node or over a specific edge at a particular time. We consider different types of queries, each defining a different variant of the Markov chain monitoring. For each variant, we design efficient algorithms for choosing the queries that make our estimates as accurate as possible. In our experiments with synthetic and real datasets we demonstrate the efficiency and the efficacy of our algorithms in a variety of settings. 13 pages, 10 figures, 1 table

Forecast aggregation combines the predictions of multiple forecasters to improve accuracy. However, the lack of knowledge about forecasters' information structure hinders optimal aggregation. Given a family of information structures, robust forecast aggregation aims to find the aggregator with minimal worst-case regret compared to the omniscient aggregator. Previous approaches for robust forecast aggregation rely on heuristic observations and parameter tuning. We propose an algorithmic framework for robust forecast aggregation. Our framework provides efficient approximation schemes for general information aggregation with a finite family of possible information structures. In the setting considered by Arieli et al. (2018) where two agents receive independent signals conditioned on a binary state, our framework also provides efficient approximation schemes by imposing Lipschitz conditions on the aggregator or discrete conditions on agents' reports. Numerical experiments demonstrate the effectiveness of our method by providing a nearly optimal aggregator in the setting considered by Arieli et al. (2018).

The adoption of artificial intelligence (AI) across industries has led to the widespread use of complex black-box models and interpretation tools for decision making. This paper proposes an adversarial framework to uncover the vulnerability of permutation-based interpretation methods for machine learning tasks, with a particular focus on partial dependence (PD) plots. This adversarial framework modifies the original black box model to manipulate its predictions for instances in the extrapolation domain. As a result, it produces deceptive PD plots that can conceal discriminatory behaviors while preserving most of the original model's predictions. This framework can produce multiple fooled PD plots via a single model. By using real-world datasets including an auto insurance claims dataset and COMPAS (Correctional Offender Management Profiling for Alternative Sanctions) dataset, our results show that it is possible to intentionally hide the discriminatory behavior of a predictor and make the black-box model appear neutral through interpretation tools like PD plots while retaining almost all the predictions of the original black-box model. Managerial insights for regulators and practitioners are provided based on the findings.