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The possibility of recognizing diverse aspects of human behavior and environmental context from passively captured data motivates its use for mental health assessment. In this paper, we analyze the contribution of different passively collected sensor data types (WiFi, GPS, Social interaction, Phone Log, Physical Activity, Audio, and Academic features) to predict daily selfreport stress and PHQ-9 depression score. First, we compute 125 mid-level features from the original raw data. These 125 features include groups of features from the different sensor data types. Then, we evaluate the contribution of each feature type by comparing the performance of Neural Network models trained with all features against Neural Network models trained with specific feature groups. Our results show that WiFi features (which encode mobility patterns) and Phone Log features (which encode information correlated with sleep patterns), provide significative information for stress and depression prediction.

In the current landscape of explanation methodologies, most predominant approaches, such as SHAP and LIME, employ removal-based techniques to evaluate the impact of individual features by simulating various scenarios with specific features omitted. Nonetheless, these methods primarily emphasize efficiency in the original context, often resulting in general inconsistencies. In this paper, we demonstrate that such inconsistency is an inherent aspect of these approaches by establishing the Impossible Trinity Theorem, which posits that interpretability, efficiency, and consistency cannot hold simultaneously. Recognizing that the attainment of an ideal explanation remains elusive, we propose the utilization of interpretation error as a metric to gauge inefficiencies and inconsistencies. To this end, we present two novel algorithms founded on the standard polynomial basis, aimed at minimizing interpretation error. Our empirical findings indicate that the proposed methods achieve a substantial reduction in interpretation error, up to 31.8 times lower when compared to alternative techniques. Code is available at //github.com/trusty-ai/efficient-consistent-explanations.

We propose an approach to 3D reconstruction via inverse procedural modeling and investigate two variants of this approach. The first option consists in the fitting set of input parameters using a genetic algorithm. We demonstrate the results of our work on tree models, complex objects, with the reconstruction of which most existing methods cannot handle. The second option allows us to significantly improve the precision by using gradients within memetic algorithm, differentiable rendering and also differentiable procedural generators. In our work we see 2 main contributions. First, we propose a method to join differentiable rendering and inverse procedural modeling. This gives us an opportunity to reconstruct 3D model more accurately than existing approaches when a small number of input images are available (even for single image). Second, we join both differentiable and non-differentiable procedural generators in a single framework which allow us to apply inverse procedural modeling to fairly complex generators: when gradient is available, reconstructions is precise, when gradient is not available, reconstruction is approximate, but always high quality without visual artifacts.

This article investigates a local discontinuous Galerkin (LDG) method for one-dimensional and two-dimensional singularly perturbed reaction-diffusion problems on a Shishkin mesh. During this process, due to the inability of the energy norm to fully capture the behavior of the boundary layers appearing in the solutions, a balanced norm is introduced. By designing novel numerical fluxes and constructing special interpolations, optimal convergences under the balanced norm are achieved in both 1D and 2D cases. Numerical experiments support the main theoretical conclusions.

In this paper the interpolating rational functions introduced by Floater and Hormann are generalized leading to a whole new family of rational functions depending on $\gamma$, an additional positive integer parameter. For $\gamma = 1$, the original Floater--Hormann interpolants are obtained. When $\gamma>1$ we prove that the new rational functions share a lot of the nice properties of the original Floater--Hormann functions. Indeed, for any configuration of nodes in a compact interval, they have no real poles, interpolate the given data, preserve the polynomials up to a certain fixed degree, and have a barycentric-type representation. Moreover, we estimate the associated Lebesgue constants in terms of the minimum ($h^*$) and maximum ($h$) distance between two consecutive nodes. It turns out that, in contrast to the original Floater-Hormann interpolants, for all $\gamma > 1$ we get uniformly bounded Lebesgue constants in the case of equidistant and quasi-equidistant nodes configurations (i.e., when $h\sim h^*$). For such configurations, as the number of nodes tends to infinity, we prove that the new interpolants ($\gamma>1$) uniformly converge to the interpolated function $f$, for any continuous function $f$ and all $\gamma>1$. The same is not ensured by the original FH interpolants ($\gamma=1$). Moreover, we provide uniform and pointwise estimates of the approximation error for functions having different degrees of smoothness. Numerical experiments illustrate the theoretical results and show a better error profile for less smooth functions compared to the original Floater-Hormann interpolants.

The Linear Model of Co-regionalization (LMC) is a very general model of multitask gaussian process for regression or classification. While its expressivity and conceptual simplicity are appealing, naive implementations have cubic complexity in the number of datapoints and number of tasks, making approximations mandatory for most applications. However, recent work has shown that under some conditions the latent processes of the model can be decoupled, leading to a complexity that is only linear in the number of said processes. We here extend these results, showing from the most general assumptions that the only condition necessary to an efficient exact computation of the LMC is a mild hypothesis on the noise model. We introduce a full parametrization of the resulting \emph{projected LMC} model, and an expression of the marginal likelihood enabling efficient optimization. We perform a parametric study on synthetic data to show the excellent performance of our approach, compared to an unrestricted exact LMC and approximations of the latter. Overall, the projected LMC appears as a credible and simpler alternative to state-of-the art models, which greatly facilitates some computations such as leave-one-out cross-validation and fantasization.

This paper explores the connections between tempering (for Sequential Monte Carlo; SMC) and entropic mirror descent to sample from a target probability distribution whose unnormalized density is known. We establish that tempering SMC is a numerical approximation of entropic mirror descent applied to the Kullback-Leibler (KL) divergence and obtain convergence rates for the tempering iterates. Our result motivates the tempering iterates from an optimization point of view, showing that tempering can be used as an alternative to Langevin-based algorithms to minimize the KL divergence. We exploit the connection between tempering and mirror descent iterates to justify common practices in SMC and propose improvements to algorithms in literature.

We provide a new characterization of both belief update and belief revision in terms of a Kripke-Lewis semantics. We consider frames consisting of a set of states, a Kripke belief relation and a Lewis selection function. Adding a valuation to a frame yields a model. Given a model and a state, we identify the initial belief set K with the set of formulas that are believed at that state and we identify either the updated belief set or the revised belief set, prompted by the input represented by formula A, as the set of formulas that are the consequent of conditionals that (1) are believed at that state and (2) have A as antecedent. We show that this class of models characterizes both the Katsuno-Mendelzon (KM) belief update functions and the AGM belief revision functions, in the following sense: (1) each model gives rise to a partial belief function that can be completed into a full KM/AGM update/revision function, and (2) for every KM/AGM update/revision function there is a model whose associated belief function coincides with it. The difference between update and revision can be reduced to two semantic properties that appear in a stronger form in revision relative to update, thus confirming the finding by Peppas et al. (1996) that, "for a fixed theory K, revising K is much the same as updating K"

Relying entirely on an attention mechanism, the Transformer introduced by Vaswani et al. (2017) achieves state-of-the-art results for machine translation. In contrast to recurrent and convolutional neural networks, it does not explicitly model relative or absolute position information in its structure. Instead, it requires adding representations of absolute positions to its inputs. In this work we present an alternative approach, extending the self-attention mechanism to efficiently consider representations of the relative positions, or distances between sequence elements. On the WMT 2014 English-to-German and English-to-French translation tasks, this approach yields improvements of 1.3 BLEU and 0.3 BLEU over absolute position representations, respectively. Notably, we observe that combining relative and absolute position representations yields no further improvement in translation quality. We describe an efficient implementation of our method and cast it as an instance of relation-aware self-attention mechanisms that can generalize to arbitrary graph-labeled inputs.