For a d-ary Boolean function Φ: {0, 1}d → {0, 1} and an assignment to its variables x = (x1, x2, . . . , xd) we consider the problem of finding those subsets of the variables that are sufficient to determine the function value with a given probability δ. This is motivated by the task of interpreting predictions of binary classifiers described as Boolean circuits, which can be seen as special cases of neural networks. We show that the problem of deciding whether such subsets of relevant variables of limited size k ≤ d exist is complete for the complexity class NPPP and thus, generally, unfeasible to solve. We then introduce a variant, in which it suffices to check whether a subset determines the function value with probability at least δ or at most δ − γ for 0 < γ < δ. This promise of a probability gap reduces the complexity to the class NPBPP. Finally, we show that finding the minimal set of relevant variables cannot be reasonably approximated, i.e. with an approximation factor d1−α for α > 0, by a polynomial time algorithm unless P = NP. This holds even with the promise of a probability gap.

Nonparametric maximum likelihood estimation is intended to infer the unknown density distribution while making as few assumptions as possible. To alleviate the over parameterization in nonparametric data fitting, smoothing assumptions are usually merged into the estimation. In this paper a novel boosting-based method is introduced to the nonparametric estimation in univariate cases. We deduce the boosting algorithm by the second-order approximation of nonparametric log-likelihood. Gaussian kernel and smooth spline are chosen as weak learners in boosting to satisfy the smoothing assumptions. Simulations and real data experiments demonstrate the efficacy of the proposed approach.

Deep Learning (DL) is a two-step classification model that consists feature learning, generating feature representations using unsupervised ways and the supervised learning stage at the last step of model using at least two hidden layers on the proposed structures by fully connected layers depending on of the artificial neural networks. The optimization of the predefined classification parameters for the supervised models eases reaching the global optimality with exact zero training error. The autoencoder (AE) models are the highly generalized ways of the unsupervised stages for the DL to define the output weights of the hidden neurons with various representations. As alternatively to the conventional Extreme Learning Machines (ELM) AE, Hessenberg decomposition-based ELM autoencoder (HessELM-AE) is a novel kernel to generate different presentations of the input data within the intended sizes of the models. The aim of the study is analyzing the performance of the novel Deep AE kernel for clinical availability on electroencephalogram (EEG) with stroke patients. The slow cortical potentials (SCP) training in stroke patients during eight neurofeedback sessions were analyzed using Hilbert-Huang Transform. The statistical features of different frequency modulations were fed into the Deep ELM model for generative AE kernels. The novel Deep ELM-AE kernels have discriminated the brain activity with high classification performances for positivity and negativity tasks in stroke patients.

Generative modeling using samples drawn from the probability distribution constitutes a powerful approach for unsupervised machine learning. Quantum mechanical systems can produce probability distributions that exhibit quantum correlations which are difficult to capture using classical models. We show theoretically that such quantum correlations provide a powerful resource for generative modeling. In particular, we provide an unconditional proof of separation in expressive power between a class of widely-used generative models, known as Bayesian networks, and its minimal quantum extension. We show that this expressivity advantage is associated with quantum nonlocality and quantum contextuality. Furthermore, we numerically test this separation on standard machine learning data sets and show that it holds for practical problems. The possibility of quantum advantage demonstrated in this work not only sheds light on the design of useful quantum machine learning protocols but also provides inspiration to draw on ideas from quantum foundations to improve purely classical algorithms.

In this study; in order to diagnose congestive heart failure (CHF) patients, non-linear secondorder difference plot (SODP) obtained from raw 256 Hz sampled frequency and windowed record with different time of ECG records are used. All of the data rows are labelled with their belongings to classify much more realistically. SODPs are divided into different radius of quadrant regions and numbers of the points fall in the quadrants are computed in order to extract feature vectors. Fisher's linear discriminant, Naive Bayes, and artificial neural network are used as classifier. The results are considered in two step validation methods as general kfold cross-validation and patient based cross-validation. As a result, it is shown that using neural network classifier with features obtained from SODP, the constructed system could distinguish normal and CHF patients with 100% accuracy rate.

Naive Bayes is a classification algorithm that works based on the Bayes theorem. Before explaining about Naive Bayes, first, we should discuss Bayes Theorem. Bayes theorem is used to find the probability of a hypothesis with given evidence. In this, using Bayes theorem we can find the probability of A, given that B occurred. A is the hypothesis and B is the evidence.

Predictions obtained by, e.g., artificial neural networks have a high accuracy but humans often perceive the models as black boxes. Insights about the decision making are mostly opaque for humans. Particularly understanding the decision making in highly sensitive areas such as healthcare or finance, is of paramount importance. The decision-making behind the black boxes requires it to be more transparent, accountable, and understandable for humans. This survey paper provides essential definitions, an overview of the different principles and methodologies of explainable Supervised Machine Learning (SML). We conduct a state-of-the-art survey that reviews past and recent explainable SML approaches and classifies them according to the introduced definitions. Finally, we illustrate principles by means of an explanatory case study and discuss important future directions.

Falls are a common problem affecting the older adults and a major public health issue. Centers for Disease Control and Prevention, and World Health Organization report that one in three adults over the age of 65 and half of the adults over 80 fall each year. In recent years, an ever-increasing range of applications have been developed to help deliver more effective falls prevention interventions. All these applications rely on a huge elderly personal database collected from hospitals, mutual health, and other organizations in caring for elderly. The information describing an elderly is continually evolving and may become obsolete at a given moment and contradict what we already know on the same person. So, it needs to be continuously checked and updated in order to restore the database consistency and then provide better service. This paper provides an outline of an Obsolete personal Information Update System (OIUS) designed in the context of the elderly-fall prevention project. Our OIUS aims to control and update in real-time the information acquired about each older adult, provide on-demand consistent information and supply tailored interventions to caregivers and fall-risk patients. The approach outlined for this purpose is based on a polynomial-time algorithm build on top of a causal Bayesian network representing the elderly data. The result is given as a recommendation tree with some accuracy level. We conduct a thorough empirical study for such a model on an elderly personal information base. Experiments confirm the viability and effectiveness of our OIUS.

Wind farms are a crucial driver toward the generation of ecological and renewable energy. Due to their rapid increase in capacity, contemporary wind farms need to adhere to strict constraints on power output to ensure stability of the electricity grid. Specifically, a wind farm controller is required to match the farm's power production with a power demand imposed by the grid operator. This is a non-trivial optimization problem, as complex dependencies exist between the wind turbines. State-of-the-art wind farm control typically relies on physics-based heuristics that fail to capture the full load spectrum that defines a turbine's health status. When this is not taken into account, the long-term viability of the farm's turbines is put at risk. Given the complex dependencies that determine a turbine's lifetime, learning a flexible and optimal control strategy requires a data-driven approach. However, as wind farms are large-scale multi-agent systems, optimizing control strategies over the full joint action space is intractable. We propose a new learning method for wind farm control that leverages the sparse wind farm structure to factorize the optimization problem. Using a Bayesian approach, based on multi-agent Thompson sampling, we explore the factored joint action space for configurations that match the demand, while considering the lifetime of turbines. We apply our method to a grid-like wind farm layout, and evaluate configurations using a state-of-the-art wind flow simulator. Our results are competitive with a physics-based heuristic approach in terms of demand error, while, contrary to the heuristic, our method prolongs the lifetime of high-risk turbines.

Approximate Bayesian Computation (ABC) now serves as one of the major strategies to perform model choice and parameter inference on models with intractable likelihoods. An essential component of ABC involves comparing a large amount of simulated data with the observed data through summary statistics. To avoid the curse of dimensionality, summary statistic selection is of prime importance, and becomes even more critical when applying ABC to mechanistic network models. Indeed, while many summary statistics can be used to encode network structures, their computational complexity can be highly variable. For large networks, computation of summary statistics can quickly create a bottleneck, making the use of ABC difficult. To reduce this computational burden and make the analysis of mechanistic network models more practical, we investigated two questions in a model choice framework. First, we studied the utility of cost-based filter selection methods to account for different summary costs during the selection process. Second, we performed selection using networks generated with a smaller number of nodes to reduce the time required for the selection step. Our findings show that computationally inexpensive summary statistics can be efficiently selected with minimal impact on classification accuracy. Furthermore, we found that networks with a smaller number of nodes can only be employed to eliminate a moderate number of summaries. While this latter finding is network specific, the former is general and can be adapted to any ABC application.