Nowadays we are witnessing a transformation of the business processes towards a more computation driven approach. The ever increasing usage of Machine Learning techniques is the clearest example of such trend. This sort of revolution is often providing advantages, such as an increase in prediction accuracy and a reduced time to obtain the results. However, these methods present a major drawback: it is very difficult to understand on what grounds the algorithm took the decision. To address this issue we consider the LIME method. We give a general background on LIME then, we focus on the stability issue: employing the method repeated times, under the same conditions, may yield to different explanations. Two complementary indices are proposed, to measure LIME stability. It is important for the practitioner to be aware of the issue, as well as to have a tool for spotting it. Stability guarantees LIME explanations to be reliable, therefore a stability assessment, made through the proposed indices, is crucial. As a case study, we apply both Machine Learning and classical statistical techniques to Credit Risk data. We test LIME on the Machine Learning algorithm and check its stability. Eventually, we examine the goodness of the explanations returned.

In multimodal traffic monitoring, we gather traffic statistics for distinct transportation modes, such as pedestrians, cars and bicycles, in order to analyze and improve people's daily mobility in terms of safety and convenience. On account of its robustness to bad light and adverse weather conditions, and inherent speed measurement ability, the radar sensor is a suitable option for this application. However, the sparse radar data from conventional commercial radars make it extremely challenging for transportation mode classification. Thus, we propose to use a high-resolution millimeter-wave(mmWave) radar sensor to obtain a relatively richer radar point cloud representation for a traffic monitoring scenario. Based on a new feature vector, we use the multivariate Gaussian mixture model (GMM) to do the radar point cloud segmentation, i.e. `point-wise' classification, in an unsupervised learning environment. In our experiment, we collected radar point clouds for pedestrians and cars, which also contained the inevitable clutter from the surroundings. The experimental results using GMM on the new feature vector demonstrated a good segmentation performance in terms of the intersection-over-union (IoU) metrics. The detailed methodology and validation metrics are presented and discussed.

Nested sampling is an efficient algorithm for the calculation of the Bayesian evidence and posterior parameter probability distributions. It is based on the step-by-step exploration of the parameter space by Monte Carlo sampling with a series of values sets called live points that evolve towards the region of interest, i.e. where the likelihood function is maximal. In presence of several local likelihood maxima, the algorithm converges with difficulty. Some systematic errors can also be introduced by unexplored parameter volume regions. In order to avoid this, different methods are proposed in the literature for an efficient search of new live points, even in presence of local maxima. Here we present a new solution based on the mean shift cluster recognition method implemented in a random walk search algorithm. The clustering recognition is integrated within the Bayesian analysis program NestedFit. It is tested with the analysis of some difficult cases. Compared to the analysis results without cluster recognition, the computation time is considerably reduced. At the same time, the entire parameter space is efficiently explored, which translates into a smaller uncertainty of the extracted value of the Bayesian evidence.

Bundling, the practice of jointly selling two or more products at a discount, is a widely used strategy in industry and a well examined concept in academia. Historically, the focus has been on theoretical studies in the context of monopolistic firms and assumed product relationships, e.g., complementarity in usage. We develop a new machine-learning-driven methodology for designing bundles in a large-scale, cross-category retail setting. We leverage historical purchases and consideration sets created from clickstream data to generate dense continuous representations of products called embeddings. We then put minimal structure on these embeddings and develop heuristics for complementarity and substitutability among products. Subsequently, we use the heuristics to create multiple bundles for each product and test their performance using a field experiment with a large retailer. We combine the results from the experiment with product embeddings using a hierarchical model that maps bundle features to their purchase likelihood, as measured by the add-to-cart rate. We find that our embeddings-based heuristics are strong predictors of bundle success, robust across product categories, and generalize well to the retailer's entire assortment.

The proposed algorithms are based on the XGBoost algorithm, which is known as one of the most powerful algorithms in the machine learning literature. Our main idea is to model the conditional mean of clinical outcome or the decision rule via additive regression trees, and use the boosting technique to estimate each single tree iteratively. Our approaches overcome the challenge of correct model specification, which is required in current parametric methods. The major contribution of our proposed algorithms is providing efficient and accurate estimation of the highly nonlinear and complex optimal individualized treatment rules that often arise in practice. Finally, we illustrate the superior performance of our algorithms by extensive simulation studies and conclude with an application to the real data from a diabetes Phase III trial. 1 Introduction Precision medicine, as an emerging medical approach for disease treatment and prevention, has received more and more attention among government, healthcare industry and academia in recent years. It is a well-known fact that there exists a significant heterogeneity for patients in response to treatments. For example, as demonstrated in [9], for patients who are infected with human immunodeficiency virus and tuberculosis, their optimal timing of antiretroviral therapy (ART) varies significantly.

Data imbalance is a major problem that affects several machine learning algorithms. Such problems are troublesome because most of the learning algorithms attempts to optimize a loss function based on error measures that do not take into account the data imbalance. Accordingly, the learning algorithm simply generates a trivial model that is biased toward predicting the most frequent class in the training data. Data augmentation techniques have been used to mitigate the data imbalance problem. However, in the case of histopathologic images (HIs), low-level as well as high-level data augmentation techniques still present performance issues when applied in the presence of inter-patient variability; whence the model tends to learn color representations, which are in fact related to the stain process. In this paper, we propose an approach capable of not only augmenting HIs database but also distributing the inter-patient variability by means of image blending using Gaussian-Laplacian pyramid. The proposed approach consists in finding the Gaussian pyramids of two images of different patients and finding the Laplacian pyramids thereof. Afterwards, the left half of one image and the right half of another are joined in each level of Laplacian pyramid, and from the joint pyramids, the original image is reconstructed. This composition, resulting from the blending process, combines stain variation of two patients, avoiding that color misleads the learning process. Experimental results on the BreakHis dataset have shown promising gains vis-\`a-vis the majority of traditional techniques presented in the literature.

--One problem found when working with satellite images is the radiometric variations across the image and different images. Intending to improve remote sensing models for the classification of burnt areas, we set two objectives. The first is to understand the relationship between feature spaces and the predictive ability of the models, allowing us to explain the differences between learning and generalization when training and testing in different datasets. We find that training on datasets built from more than one image provides models that generalize better . These results are explained by visualizing the dispersion of values on the feature space. The second objective is to evolve hyper-features that improve the performance of different classifiers on a variety of test sets. We find the hyper-features to be beneficial, and obtain the best models with XGBoost, even if the hyper-features are optimized for a different method. Deforestation has serious implications on biodiversity, on rural communities that depend on forests for survival, and on greenhouse gas emissions that drive the global climate. The machine learning (ML) community can help by providing predictive models that, after learning from a small sample of an image, can automatically classify the whole image. Although previous ML work in forest monitoring has shown good results, the predictive models are often applied on the same location where they were learnt, i.e., the models are trained and tested in samples from the same dataset (e.g., [1]) or time series from the same area (e.g., [2]).

--In this paper, we introduce a Deep Convolutional Analysis Dictionary Model (DeepCAM) by learning convolutional dictionaries instead of unstructured dictionaries as in the case of deep analysis dictionary model introduced in the companion paper . Convolutional dictionaries are more suitable for processing high-dimensional signals like for example images and have only a small number of free parameters. By exploiting the properties of a convolutional dictionary, we present an efficient convolutional analysis dictionary learning approach. A L-layer DeepCAM consists of L layers of convolutional analysis dictionary and element-wise soft-thresholding pairs and a single layer of convolutional synthesis dictionary. Similar to DeepAM, each convolutional analysis dictionary is composed of a convolutional Information Preserving Analysis Dictionary (IPAD) and a con-volutional Clustering Analysis Dictionary (CAD). The IPAD and the CAD are learned using variations of the proposed learning algorithm. We demonstrate that DeepCAM is an effective multi-layer convolutional model and, on single image super-resolution, achieves performance comparable with other methods while also showing good generalization capabilities. ONVOLUTIONAL dictionary learning has attracted increasing interests in signal and image processing communities as it leads to a more elegant framework for high-dimensional signal analysis. An advantage of convolutional dictionaries [1]-[13] is that they can take the high-dimensional signal as input for sparse representation and processing, whereas traditional approaches [14]-[20] have to divide the high-dimensional signal into overlapping low-dimensional patches and perform sparse representation on each patch independently. It is a structured dictionary and can be represented as a concatenation of Toeplitz matrices where each Toeplitz matrix is constructed using the taps of a filter and the usual assumption is that the filters are with compact support. So a convolutional dictionary is effective for processing high-dimensional signals while also restraining the number of free parameters. To achieve efficient convolutional dictionary learning, the convolutional dictionary is usually modelled as a concatenation of circulant matrices [1]-[6] by assuming a periodic boundary condition on the signals. As all circulant matrices share the same set of eigenvectors which is the Discrete Fourier Transform (DFT) matrix, a circular convolution can be therefore represented as a multiplication in Fourier domain and can be efficiently implemented using Fast Fourier Transform (FFT). However, using a circulant matrix to approximate a general Toeplitz matrix may lead to boundary artifacts [3], [21], [22] especially when the boundary region is large. A multi-layer convolutional dictionary model is able to represent multiple levels of abstraction of the input signal.

This tutorial paper focuses on the variants of the bottleneck problem taking an information theoretic perspective and discusses practical methods to solve it, as well as its connection to coding and learning aspects. The intimate connections of this setting to remote source-coding under logarithmic loss distortion measure, information combining, common reconstruction, the Wyner-Ahlswede-Korner problem, the efficiency of investment information, as well as, generalization, variational inference, representation learning, autoencoders, and others are highlighted. We discuss its extension to the distributed information bottleneck problem with emphasis on the Gaussian model and highlight the basic connections to the uplink Cloud Radio Access Networks (CRAN) with oblivious processing. For this model, the optimal trade-offs between relevance (i.e., information) and complexity (i.e., rates) in the discrete and vector Gaussian frameworks is determined. In the concluding outlook, some interesting problems are mentioned such as the characterization of the optimal inputs ("features") distributions under power limitations maximizing the "relevance" for the Gaussian information bottleneck, under "complexity" constraints.

--Intrinsic dimensionality (ID) is one of the most fundamental characteristics of multidimensional data point clouds. Knowing ID is crucial to choose the appropriate machine learning approach as well as to understand its behavior and validate it. ID can be computed globally for the whole data distribution, or estimated locally in a point. In this paper, we introduce new local estimators of ID based on linear separability of multidimensional data point clouds, which is one of the manifestations of concentration of measure. We empirically study the properties of these measures and compare them with other recently introduced ID estimators exploiting various effects of measure concentration. Observed differences in the behaviour of different estimators can be used to anticipate their behaviour in practical applications. Datasets used in applications of machine learning frequently contain objects characterized by thousands and even millions of features.