Solving inverse problems is central to geosciences and remote sensing. Radiative transfer models (RTMs) represent mathematically the physical laws which govern the phenomena in remote sensing applications (forward models). The numerical inversion of the RTM equations is a challenging and computationally demanding problem, and for this reason, often the application of a nonlinear statistical regression is preferred. In general, regression models predict the biophysical parameter of interest from the corresponding received radiance. However, this approach does not employ the physical information encoded in the RTMs. An alternative strategy, which attempts to include the physical knowledge, consists in learning a regression model trained using data simulated by an RTM code. In this work, we introduce a nonlinear nonparametric regression model which combines the benefits of the two aforementioned approaches. The inversion is performed taking into account jointly both real observations and RTM-simulated data. The proposed Joint Gaussian Process (JGP) provides a solid framework for exploiting the regularities between the two types of data. The JGP automatically detects the relative quality of the simulated and real data, and combines them accordingly. This occurs by learning an additional hyper-parameter w.r.t. a standard GP model, and fitting parameters through maximizing the pseudo-likelihood of the real observations. The resulting scheme is both simple and robust, i.e., capable of adapting to different scenarios. The advantages of the JGP method compared to benchmark strategies are shown considering RTM-simulated and real observations in different experiments. Specifically, we consider leaf area index (LAI) retrieval from Landsat data combined with simulated data generated by the PROSAIL model.

Ensemble techniques are powerful approaches that combine several weak learners to build a stronger one. As a meta learning framework, ensemble techniques can easily be applied to many machine learning techniques. In this paper we propose a neural network extended with an ensemble loss function for text classification. The weight of each weak loss function is tuned within the training phase through the gradient propagation optimization method of the neural network. The approach is evaluated on several text classification datasets. We also evaluate its performance in various environments with several degrees of label noise. Experimental results indicate an improvement of the results and strong resilience against label noise in comparison with other methods.

We consider a sparse high dimensional regression model where the goal is to recover a k-sparse unknown vector \beta^* from n noisy linear observations of the form Y=X\beta^*+W \in R^n where X \in R^{n \times p} has iid N(0,1) entries and W \in R^n has iid N(0,\sigma^2) entries. Under certain assumptions on the parameters, an intriguing assymptotic gap appears between the minimum value of n, call it n^*, for which the recovery is information theoretically possible, and the minimum value of n, call it n_{alg}, for which an efficient algorithm is known to provably recover \beta^*. In a recent paper it was conjectured that the gap is not artificial, in the sense that for sample sizes n \in [n^*,n_{alg}] the problem is algorithmically hard. We support this conjecture in two ways. Firstly, we show that a well known recovery mechanism called Basis Pursuit Denoising Scheme provably fails to \ell_2-stably recover the vector when n \in [n^*,c n_{alg}], for some sufficiently small constant c>0. Secondly, we establish that n_{alg}, up to a multiplicative constant factor, is a phase transition point for the appearance of a certain Overlap Gap Property (OGP) over the space of k-sparse vectors. The presence of such an Overlap Gap Property phase transition, which originates in statistical physics, is known to provide evidence of an algorithmic hardness. Finally we show that if n>C n_{alg} for some large enough constant C>0, a very simple algorithm based on a local search improvement is able to infer correctly the support of the unknown vector \beta^*, adding it to the list of provably successful algorithms for the high dimensional linear regression problem.

In many settings, it is important that a model be capable of providing reasons for its predictions (i.e., the model must be interpretable). However, the model's reasoning may not conform with well-established knowledge. In such cases, while interpretable, the model lacks \textit{credibility}. In this work, we formally define credibility in the linear setting and focus on techniques for learning models that are both accurate and credible. In particular, we propose a regularization penalty, expert yielded estimates (EYE), that incorporates expert knowledge about well-known relationships among covariates and the outcome of interest. We give both theoretical and empirical results comparing our proposed method to several other regularization techniques. Across a range of settings, experiments on both synthetic and real data show that models learned using the EYE penalty are significantly more credible than those learned using other penalties. Applied to a large-scale patient risk stratification task, our proposed technique results in a model whose top features overlap significantly with known clinical risk factors, while still achieving good predictive performance.

Theoretical studies have proven that the Hilbert space has remarkable performance in many fields of applications. Frames in tensor product of Hilbert spaces were introduced to generalize the inner product to high-order tensors. However, these techniques require tensor decomposition which could lead to the loss of information and it is a NP-hard problem to determine the rank of tensors. Here, we present a new framework, namely matrix Hilbert space to perform a matrix inner product space when data observations are represented as matrices. We preserve the structure of initial data and multi-way correlation among them is captured in the process. In addition, we extend the reproducing kernel Hilbert space (RKHS) to reproducing kernel matrix Hilbert space (RKMHS) and propose an equivalent condition of the space uses of the certain kernel function. A new family of kernels is introduced in our framework to apply the classifier of Support Tensor Machine(STM) and comparative experiments are performed on a number of real-world datasets to support our contributions.

Stein variational gradient descent (SVGD) is a deterministic sampling algorithm that iteratively transports a set of particles to approximate given distributions, based on a gradient-based update that guarantees to optimally decrease the KL divergence within a function space. This paper develops the first theoretical analysis on SVGD. We establish that the empirical measures of the SVGD samples weakly converge to the target distribution, and show that the asymptotic behavior of SVGD is characterized by a nonlinear Fokker-Planck equation known as Vlasov equation in physics. We develop a geometric perspective that views SVGD as a gradient flow of the KL divergence functional under a new metric structure on the space of distributions induced by Stein operator.

This preprint has been reviewed and recommended by Peer Community In Evolutionary Biology (http://dx.doi.org/10.24072/pci.evolbiol.100036). Approximate Bayesian computation (ABC) has grown into a standard methodology that manages Bayesian inference for models associated with intractable likelihood functions. Most ABC implementations require the preliminary selection of a vector of informative statistics summarizing raw data. Furthermore, in almost all existing implementations, the tolerance level that separates acceptance from rejection of simulated parameter values needs to be calibrated. We propose to conduct likelihood-free Bayesian inferences about parameters with no prior selection of the relevant components of the summary statistics and bypassing the derivation of the associated tolerance level. The approach relies on the random forest methodology of Breiman (2001) applied in a (non parametric) regression setting. We advocate the derivation of a new random forest for each component of the parameter vector of interest. When compared with earlier ABC solutions, this method offers significant gains in terms of robustness to the choice of the summary statistics, does not depend on any type of tolerance level, and is a good trade-off in term of quality of point estimator precision and credible interval estimations for a given computing time. We illustrate the performance of our methodological proposal and compare it with earlier ABC methods on a Normal toy example and a population genetics example dealing with human population evolution. All methods designed here have been incorporated in the R package abcrf (version 1.7) available on CRAN.

Computer Vision and machine learning methods were previously used to reveal screen presence of genders in TV and movies [4]. In this work, using head pose, gender detection, and skin color estimation techniques, we demonstrate that the gender disparity in TV in a South Asian country such as Bangladesh exhibits unique characteristics and is sometimes counterintuitive to popular perception. We demonstrate a noticeable discrepancy in female screen presence in Bangladeshi TV advertisements and political talk shows. Further, contrary to popular hypotheses, we demonstrate that lighter-toned skin colors are less prevalent than darker complexions, and additionally, quantifiable body language markers do not provide conclusive insights about gender dynamics. Overall, these gender portrayal parameters reveal the different layers of onscreen gender politics and can help direct incentives to address existing disparities in a nuanced and targeted manner.

The goal of imitation learning is to mimic expert behavior without access to an explicit reward signal. Expert demonstrations provided by humans, however, often show significant variability due to latent factors that are typically not explicitly modeled. In this paper, we propose a new algorithm that can infer the latent structure of expert demonstrations in an unsupervised way. Our method, built on top of Generative Adversarial Imitation Learning, can not only imitate complex behaviors, but also learn interpretable and meaningful representations of complex behavioral data, including visual demonstrations. In the driving domain, we show that a model learned from human demonstrations is able to both accurately reproduce a variety of behaviors and accurately anticipate human actions using raw visual inputs. Compared with various baselines, our method can better capture the latent structure underlying expert demonstrations, often recovering semantically meaningful factors of variation in the data.

We used redescription mining to find interpretable rules revealing associations between those determinants that provide insights about the Alzheimer's disease (AD). We extended the CLUS-RM redescription mining algorithm to a constraint-based redescription mining (CBRM) setting, which enables several modes of targeted exploration of specific, user-constrained associations. Redescription mining enabled finding specific constructs of clinical and biological attributes that describe many groups of subjects of different size, homogeneity and levels of cognitive impairment. We confirmed some previously known findings. However, in some instances, as with the attributes: testosterone, the imaging attribute Spatial Pattern of Abnormalities for Recognition of Early AD, as well as the levels of leptin and angiopoietin-2 in plasma, we corroborated previously debatable findings or provided additional information about these variables and their association with AD pathogenesis. Applying redescription mining on ADNI data resulted with the discovery of one largely unknown attribute: the Pregnancy-Associated Protein-A (PAPP-A), which we found highly associated with cognitive impairment in AD. Statistically significant correlations (p <= 0.01) were found between PAPP-A and various different clinical tests. The high importance of this finding lies in the fact that PAPP-A is a metalloproteinase, known to cleave insulin-like growth factor binding proteins. Since it also shares similar substrates with A Disintegrin and the Metalloproteinase family of enzymes that act as {\alpha}-secretase to physiologically cleave amyloid precursor protein (APP) in the non-amyloidogenic pathway, it could be directly involved in the metabolism of APP very early during the disease course. Therefore, further studies should investigate the role of PAPP-A in the development of AD more thoroughly.