In this work, we propose the first quantum Ans\"atze for the statistical relational learning on knowledge graphs using parametric quantum circuits. We introduce two types of variational quantum circuits for knowledge graph embedding. Inspired by the classical representation learning, we first consider latent features for entities as coefficients of quantum states, while predicates are characterized by parametric gates acting on the quantum states. For the first model, the quantum advantages disappear when it comes to the optimization of this model. Therefore, we introduce a second quantum circuit model where embeddings of entities are generated from parameterized quantum gates acting on the pure quantum state. The benefit of the second method is that the quantum embeddings can be trained efficiently meanwhile preserving the quantum advantages. We show the proposed methods can achieve comparable results to the state-of-the-art classical models, e.g., RESCAL, DistMult. Furthermore, after optimizing the models, the complexity of inductive inference on the knowledge graphs might be reduced with respect to the number of entities.

Learn about CART in this guest post by Jillur Quddus, a lead technical architect, polyglot software engineer and data scientist with over 10 years of hands-on experience in architecting and engineering distributed, scalable, high-performance, and secure solutions used to combat serious organized crime, cybercrime, and fraud. Although both linear regression models allow and logistic regression models allow us to predict a categorical outcome, both of these models assume a linear relationship between variables. Classification and Regression Trees (CART) overcome this problem by generating Decision Trees. These decision trees can then be traversed to come to a final decision, where the outcome can either be numerical (regression trees) or categorical (classification trees). When traversing decision trees, start at the top. Thereafter, traverse left for yes, or positive responses, and traverse right for no, or negative responses.

Would people who are strong in math be good in machine learning? Certainly having a strong background in mathematics will make it easier to understand machine learning at a conceptual level. When someone introduces you to the inference function in logistic regression, you'll say, "Hey, that's just linear algebra!" But surely deep learning must be something new? Not harder, just more (thank God for automatic differentiation). Supposing you did well in those undergrad classes, machine learning should come easy enough at first.

The objective of this work is to study the applicability of various Machine Learning algorithms for prediction of some rock properties which geoscientists usually define due to special lab analysis. We demonstrate that these special properties can be predicted only basing on routine core analysis (RCA) data. To validate the approach core samples from the reservoir with soluble rock matrix components (salts) were tested within 100+ laboratory experiments. The challenge of the experiments was to characterize the rate of salts in cores and alteration of porosity and permeability after reservoir desalination due to drilling mud or water injection. For these three measured characteristics, we developed the relevant predictive models, which were based on the results of RCA and data on coring depth and top and bottom depths of productive horizons. To select the most accurate Machine Learning algorithm a comparative analysis has been performed. It was shown that different algorithms work better in different models. However, two hidden layers Neural network has demonstrated the best predictive ability and generalizability for all three rock characteristics jointly. The other algorithms, such as Support Vector Machine and Linear Regression, also worked well on the dataset, but in particular cases. Overall, the applied approach allows predicting the alteration of porosity and permeability during desalination in porous rocks and also evaluating salt concentration without direct measurements in a laboratory. This work also shows that developed approaches could be applied for prediction of other rock properties (residual brine and oil saturations, relative permeability, capillary pressure, and others), which laboratory measurements are time-consuming and expensive.

Although deep convolutional networks have achieved improved performance in many natural language tasks, they have been treated as black boxes because they are difficult to interpret. Especially, little is known about how they represent language in their intermediate layers. In an attempt to understand the representations of deep convolutional networks trained on language tasks, we show that individual units are selectively responsive to specific morphemes, words, and phrases, rather than responding to arbitrary and uninterpretable patterns. In order to quantitatively analyze such an intriguing phenomenon, we propose a concept alignment method based on how units respond to the replicated text. We conduct analyses with different architectures on multiple datasets for classification and translation tasks and provide new insights into how deep models understand natural language.

Nowadays the increasing and rapid progress of technology and the availability of electronic documents from a variety of sources have made a huge amount of textual data available. Hence, one of the prominent research topics of statistical andmachine learning communities is to provide suitable and feasible methods to extract high-quality information from unstructured textual data (Lata and Loar, 2018) for the different purposes of clustering, classification and document retrieval (Khan et al., 2010). This work originates from an empirical problem of classification of the content ofcalls made to the customer service of an important mobile phone company inItaly. The received calls are written down by an operator and classified into relevant classes (e.g.

Most work on interpretability in machine learning has focused on designing either inherently interpretable models, that typically trade-off interpretability for accuracy, or post-hoc explanation systems, that lack guarantees about their explanation quality. We propose an alternative to these approaches by directly regularizing a black-box model for interpretability at training time. Our approach explicitly connects three key aspects of interpretable machine learning: the model's innate explainability, the explanation system used at test time, and the metrics that measure explanation quality. Our regularization results in substantial (up to orders of magnitude) improvement in terms of explanation fidelity and stability metrics across a range of datasets, models, and black-box explanation systems. Remarkably, our regularizers also slightly improve predictive accuracy on average across the nine datasets we consider. Further, we show that the benefits of our novel regularizers on explanation quality provably generalize to unseen test points.

V alidation is one of the most important aspects of clustering, but most approaches have been batch methods. Recently, interest has grown in providing incremental alternatives. This paper extends the incremental cluster validity index (iCVI) family to include incremental versions of Calinski-Harabasz (iCH), I index and Pakhira-Bandyopadhyay-Maulik (iI and iPBM), Silhouette (iSIL), Negentropy Increment (iNI), Representative Cross Information Potential (irCIP) and Representative Cross Entropy (irH), and Conn Index (iConn Index). Additionally, the effect of under-and over-partitioning on the behavior of these six iCVIs, the Partition Separation (PS) index, as well as two other recently developed iCVIs (incremental Xie-Beni (iXB) and incremental Davies-Bouldin (iDB)) was examined through a comparative study. Experimental results using fuzzy adaptive resonance theory (ART)-based clustering methods showed that while evidence of most under-partitioning cases could be inferred from the behaviors of all these iCVIs, over-partitioning was found to be a more challenging scenario indicated only by the iConn Index. The expansion of incremental validity indices provides significant novel opportunities for assessing and interpreting the results of unsupervised learning. L. E. Brito da Silva is with the Applied Computational Intelligence Laboratory, Department of Electrical and Computer Engineering, Missouri University of Science and Technology, Rolla, MO 65409 USA, and also with the CAPES Foundation, Ministry of Education of Brazil, Bras ılia, DF 70040-020, Brazil (email: leonardoenzo@ieee.org). N. M. Melton is with the Applied Computational Intelligence Laboratory, Department of Electrical and Computer Engineering, Missouri University of Science and Technology, Rolla, MO 65409 USA (email: niklasmelton@ieee.org). D. C. Wunsch II is with the Applied Computational Intelligence Laboratory, Department of Electrical and Computer Engineering, Missouri University of Science and Technology, Rolla, MO 65409 USA (email: wunsch@ieee.org). I NTRODUCTION Cluster validation [1] is a critical topic in cluster analysis.

They can be basically defined as a multi-layer stack of algorithms or modules able to gradually learn a huge number of parameters in an architecture composed by multiple nonlinear transformations (LeCun et al., 2015). Typically, and for historical reasons, a structure for deep learning is identified with advanced neural networks: deep Feed Forward, Recurrent, Auto-encoder, Convolution neural networks are very effective and used algorithms of deep learning (Schmidhuber, 2015). They demonstrated to be particularly successful in supervised classification problems arising in several fields such as image and speech recognition, gene expression data, topic classification. When the aim is uncovering unknown classes in a unsupervised classification perspective, important methods of deep learning have been developed along the lines of mixture modeling, because of their ability to decompose a heterogeneous collection of units into a finite number of subgroups with homogeneous structures (Fraley and Raftery, 2002; McLachlan and Peel, 2000). In this direction, van den Oord and Schrauwen (2014) proposed Multilayer Gaussian Mixture Models for modeling natural images; Tang et al. (2012) defined deep mixture of factor analyzers with a greedy layer-wise learning algorithm able to learn each layer at a time. Viroli and McLachlan (2019) developed a general framework for Deep Gaussian mixture models that generalizes and encompasses the previous strategies and several flexible model-based clustering methods such as mixtures of mixture models (Li, 2005), mixtures of Factor Analyzers (McLachlan et al., 2003), mixtures of factor analyzers with common factor loadings (Baek et al., 2010), heteroscedastic factor mixture analysis (Montanari and Viroli, 2010) and mixtures of factor mixture analyzers introduced by Viroli (2010). A general'take-home-message' coming from the existing deep clustering strategies is that deep methods vs shallow ones appear to be very efficient and powerful tools especially for complex high-dimensional data; on the contrary, for simple and small data structures, a deep learning strategy cannot improve performance of simpler and conventional methods or, to better say, it is like to use a'sledgehammer to crack a nut'. The motivating problem behind this work derives from ticket data (i.e.

The performance of policy gradient methods is sensitive to hyperparameter settings that must be tuned for any new application. Widely used grid search methods for tuning hyperparameters are sample inefficient and computationally expensive. More advanced methods like Population Based Training (Jaderberg et al., 2017) that learn optimal schedules for hyperparameters instead of fixed settings canyield better results, but are also sample inefficient and computationally expensive. In this paper, we propose Hyperparameter Optimisation on the Fly (HOOF), a gradient-free meta-learning algorithm that can automatically learn an optimal schedule for hyperparameters that affect the policy updatedirectly through the gradient. The main idea is to use existing trajectories sampled by the policy gradient method to optimise a one-step improvement objective,yielding a sample and computationally efficientalgorithm that is easy to implement. Our experimental results across multiple domains and algorithms show that using HOOF to learn these hyperparameter schedules leads to faster learning with improved performance.