In our previous work we have shown how Bayesian networks can be used for adaptive testing of student skills. Later, we have taken the advantage of monotonicity restrictions in order to learn models fitting data better. This article provides a synergy between these two phases as it evaluates Bayesian network models used for computerized adaptive testing and learned with a recently proposed monotonicity gradient algorithm. This learning method is compared with another monotone method, the isotonic regression EM algorithm. The quality of methods is empirically evaluated on a large data set of the Czech National Mathematics Exam. Besides advantages of adaptive testing approach we observed also advantageous behavior of monotonic methods, especially for small learning data set sizes. Another novelty of this work is the use of the reliability interval of the score distribution, which is used to predict student's final score and grade. In the experiments we have clearly shown we can shorten the test while keeping its reliability. We have also shown that the monotonicity increases the prediction quality with limited training data sets. The monotone model learned by the gradient method has a lower question prediction quality than unrestricted models but it is better in the main target of this application, which is the student score prediction. It is an important observation that a mere optimization of the model likelihood or the prediction accuracy do not necessarily lead to a model that describes best the student.

Curation of large fully supervised datasets has become one of the major roadblocks for machine learning. Weak supervision provides an alternative to supervised learning by training with cheap, noisy, and possibly correlated labeling functions from varying sources. The key challenge in weakly supervised learning is combining the different weak supervision signals while navigating misleading correlations in their errors. In this paper, we propose a simple data-free approach for combining weak supervision signals by defining a constrained space for the possible labels of the weak signals and training with a random labeling within this constrained space. Our method is efficient and stable, converging after a few iterations of gradient descent. We prove theoretical conditions under which the worst-case error of the randomized label decreases with the rank of the linear constraints. We show experimentally that our method outperforms other weak supervision methods on various text- and image-classification tasks.

Many real-world applications involve black-box optimization of multiple objectives using continuous function approximations that trade-off accuracy and resource cost of evaluation. For example, in rocket launching research, we need to find designs that trade-off return-time and angular distance using continuous-fidelity simulators (e.g., varying tolerance parameter to trade-off simulation time and accuracy) for design evaluations. The goal is to approximate the optimal Pareto set by minimizing the cost for evaluations. In this paper, we propose a novel approach referred to as information-Theoretic Multi-Objective Bayesian Optimization with Continuous Approximations (iMOCA)} to solve this problem. The key idea is to select the sequence of input and function approximations for multiple objectives which maximize the information gain per unit cost for the optimal Pareto front. Our experiments on diverse synthetic and real-world benchmarks show that iMOCA significantly improves over existing single-fidelity methods.

Concept drift is a phenomenon in which the distribution of a data stream changes over time in unforeseen ways, causing prediction models built on historical data to become inaccurate. While a variety of automated methods have been developed to identify when concept drift occurs, there is limited support for analysts who need to understand and correct their models when drift is detected. In this paper, we present a visual analytics method, DriftVis, to support model builders and analysts in the identification and correction of concept drift in streaming data. DriftVis combines a distribution-based drift detection method with a streaming scatterplot to support the analysis of drift caused by the distribution changes of data streams and to explore the impact of these changes on the model's accuracy. A quantitative experiment and two case studies on weather prediction and text classification have been conducted to demonstrate our proposed tool and illustrate how visual analytics can be used to support the detection, examination, and correction of concept drift.

Data-driven design of mechanical metamaterials is an increasingly popular method to combat costly physical simulations and immense, often intractable, geometrical design spaces. Using a precomputed dataset of unit cells, a multiscale structure can be quickly filled via combinatorial search algorithms, and machine learning models can be trained to accelerate the process. However, the dependence on data induces a unique challenge: An imbalanced dataset containing more of certain shapes or physical properties can be detrimental to the efficacy of data-driven approaches. In answer, we posit that a smaller yet diverse set of unit cells leads to scalable search and unbiased learning. To select such subsets, we propose METASET, a methodology that 1) uses similarity metrics and positive semi-definite kernels to jointly measure the closeness of unit cells in both shape and property spaces, and 2) incorporates Determinantal Point Processes for efficient subset selection. Moreover, METASET allows the trade-off between shape and property diversity so that subsets can be tuned for various applications. Through the design of 2D metamaterials with target displacement profiles, we demonstrate that smaller, diverse subsets can indeed improve the search process as well as structural performance. By eliminating inherent overlaps in a dataset of 3D unit cells created with symmetry rules, we also illustrate that our flexible method can distill unique subsets regardless of the metric employed. Our diverse subsets are provided publicly for use by any designer.

We develop heuristic interpolation methods for the function $t \mapsto \operatorname{trace}\left( (\mathbf{A} + t \mathbf{B})^{-1} \right)$, where the matrices $\mathbf{A}$ and $\mathbf{B}$ are symmetric and positive definite and $t$ is a real variable. This function is featured in many applications in statistics, machine learning, and computational physics. The presented interpolation functions are based on the modification of a sharp upper bound that we derive for this function, which is a new trace inequality for matrices. We demonstrate the accuracy and performance of the proposed method with numerical examples, namely, the marginal maximum likelihood estimation for linear Gaussian process regression and the estimation of the regularization parameter of ridge regression with the generalized cross-validation method.

This thesis focuses on the research and development of the Hemodynamic Tissue Signature (HTS) method: an unsupervised machine learning approach to describe the vascular heterogeneity of glioblastomas by means of perfusion MRI analysis. The HTS builds on the concept of habitats. An habitat is defined as a sub-region of the lesion with a particular MRI profile describing a specific physiological behavior. The HTS method delineates four habitats within the glioblastoma: the High Angiogenic Tumor (HAT) habitat, as the most perfused region of the enhancing tumor; the Low Angiogenic Tumor (LAT) habitat, as the region of the enhancing tumor with a lower angiogenic profile; the potentially Infiltrated Peripheral Edema (IPE) habitat, as the non-enhancing region adjacent to the tumor with elevated perfusion indexes; and the Vasogenic Peripheral Edema (VPE) habitat, as the remaining edema of the lesion with the lowest perfusion profile. The results of this thesis have been published in ten scientific contributions, including top-ranked journals and conferences in the areas of Medical Informatics, Statistics and Probability, Radiology & Nuclear Medicine, Machine Learning and Data Mining and Biomedical Engineering. An industrial patent registered in Spain (ES201431289A), Europe (EP3190542A1) and EEUU (US20170287133A1) was also issued, summarizing the efforts of the thesis to generate tangible assets besides the academic revenue obtained from research publications. Finally, the methods, technologies and original ideas conceived in this thesis led to the foundation of ONCOANALYTICS CDX, a company framed into the business model of companion diagnostics for pharmaceutical compounds, thought as a vehicle to facilitate the industrialization of the ONCOhabitats technology.

Independent sociological polls are forbidden in Belarus. Online polls performed without sound scientific rigour do not yield representative results. Yet, both inside and outside Belarus it is of great importance to obtain precise estimates of the ratings of all candidates. These ratings could function as reliable proxies for the election's outcomes. We conduct an independent poll based on the combination of the data collected via Viber and on the streets of Belarus. The Viber and the street data samples consist of almost 45000 and 1150 unique observations respectively. Bayesian regressions with poststratification were build to estimate ratings of the candidates and rates of early voting turnout for the population as a whole and within various focus subgroups. We show that both the officially announced results of the election and early voting rates are highly improbable. With a probability of at least 95%, Sviatlana Tikhanouskaya's rating lies between 75% and 80%, whereas Aliaksandr Lukashenka's rating lies between 13% and 18% and early voting rate predicted by the method ranges from 9% to 13% of those who took part in the election. These results contradict the officially announced outcomes, which are 10.12%, 80.11%, and 49.54% respectively and lie far outside even the 99.9% credible intervals predicted by our model. The only marginal groups of people where the upper bounds of the 99.9% credible intervals of the rating of Lukashenka are above 50% are people older than 60 and uneducated people. For all other marginal subgroups, including rural residents, even the upper bounds of 99.9% credible intervals for Lukashenka are far below 50%. The same is true for the population as a whole. Thus, with a probability of at least 99.9% Lukashenka could not have had enough electoral support to win the 2020 presidential election in Belarus.

Plants are fundamentally important to life. Key research areas in plant science include plant species identification, weed classification using hyper spectral images, monitoring plant health and tracing leaf growth, and the semantic interpretation of leaf information. Botanists easily identify plant species by discriminating between the shape of the leaf, tip, base, leaf margin and leaf vein, as well as the texture of the leaf and the arrangement of leaflets of compound leaves. Because of the increasing demand for experts and calls for biodiversity, there is a need for intelligent systems that recognize and characterize leaves so as to scrutinize a particular species, the diseases that affect them, the pattern of leaf growth, and so on. We review several image processing methods in the feature extraction of leaves, given that feature extraction is a crucial technique in computer vision. As computers cannot comprehend images, they are required to be converted into features by individually analysing image shapes, colours, textures and moments. Images that look the same may deviate in terms of geometric and photometric variations. In our study, we also discuss certain machine learning classifiers for an analysis of different species of leaves.

This paper shows that dropout training in Generalized Linear Models is the minimax solution of a two-player, zero-sum game where an adversarial nature corrupts a statistician's covariates using a multiplicative nonparametric errors-in-variables model. In this game---known as a Distributionally Robust Optimization problem---nature's least favorable distribution is dropout noise, where nature independently deletes entries of the covariate vector with some fixed probability $\delta$. Our decision-theoretic analysis shows that dropout training---the statistician's minimax strategy in the game---indeed provides out-of-sample expected loss guarantees for distributions that arise from multiplicative perturbations of in-sample data. This paper also provides a novel, parallelizable, Unbiased Multi-Level Monte Carlo algorithm to speed-up the implementation of dropout training. Our algorithm has a much smaller computational cost compared to the naive implementation of dropout, provided the number of data points is much smaller than the dimension of the covariate vector.