Computing a Nonnegative Matrix Factorization -- Provably

In the Nonnegative Matrix Factorization (NMF) problem we are given an $n \times m$ nonnegative matrix $M$ and an integer $r > 0$. Our goal is to express $M$ as $A W$ where $A$ and $W$ are nonnegative matrices of size $n \times r$ and $r \times m$ respectively. In some applications, it makes sense to ask instead for the product $AW$ to approximate $M$ -- i.e. (approximately) minimize \norm{M - AW}_F where \norm{}_F denotes the Frobenius norm; we refer to this as Approximate NMF. This problem has a rich history spanning quantum mechanics, probability theory, data analysis, polyhedral combinatorics, communication complexity, demography, chemometrics, etc. In the past decade NMF has become enormously popular in machine learning, where $A$ and $W$ are computed using a variety of local search heuristics. Vavasis proved that this problem is NP-complete. We initiate a study of when this problem is solvable in polynomial time: 1. We give a polynomial-time algorithm for exact and approximate NMF for every constant $r$. Indeed NMF is most interesting in applications precisely when $r$ is small. 2. We complement this with a hardness result, that if exact NMF can be solved in time $(nm)^{o(r)}$, 3-SAT has a sub-exponential time algorithm. This rules out substantial improvements to the above algorithm. 3. We give an algorithm that runs in time polynomial in $n$, $m$ and $r$ under the separablity condition identified by Donoho and Stodden in 2003. The algorithm may be practical since it is simple and noise tolerant (under benign assumptions). Separability is believed to hold in many practical settings. To the best of our knowledge, this last result is the first example of a polynomial-time algorithm that provably works under a non-trivial condition on the input and we believe that this will be an interesting and important direction for future work.Comment: 29 pages, 3 figure

USING PROBABILISTIC GRAPHICAL MODELS TO DRAW INFERENCES IN SENSOR NETWORKS WITH TRACKING APPLICATIONS

Sensor networks have been an active research area in the past decade due to the variety of their applications. Many research studies have been conducted to solve the problems underlying the middleware services of sensor networks, such as self-deployment, self-localization, and synchronization. With the provided middleware services, sensor networks have grown into a mature technology to be used as a detection and surveillance paradigm for many real-world applications. The individual sensors are small in size. Thus, they can be deployed in areas with limited space to make unobstructed measurements in locations where the traditional centralized systems would have trouble to reach. However, there are a few physical limitations to sensor networks, which can prevent sensors from performing at their maximum potential. Individual sensors have limited power supply, the wireless band can get very cluttered when multiple sensors try to transmit at the same time. Furthermore, the individual sensors have limited communication range, so the network may not have a 1-hop communication topology and routing can be a problem in many cases. Carefully designed algorithms can alleviate the physical limitations of sensor networks, and allow them to be utilized to their full potential. Graphical models are an intuitive choice for designing sensor network algorithms. This thesis focuses on a classic application in sensor networks, detecting and tracking of targets. It develops feasible inference techniques for sensor networks using statistical graphical model inference, binary sensor detection, events isolation and dynamic clustering. The main strategy is to use only binary data for rough global inferences, and then dynamically form small scale clusters around the target for detailed computations. This framework is then extended to network topology manipulation, so that the framework developed can be applied to tracking in different network topology settings. Finally the system was tested in both simulation and real-world environments. The simulations were performed on various network topologies, from regularly distributed networks to randomly distributed networks. The results show that the algorithm performs well in randomly distributed networks, and hence requires minimum deployment effort. The experiments were carried out in both corridor and open space settings. A in-home falling detection system was simulated with real-world settings, it was setup with 30 bumblebee radars and 30 ultrasonic sensors driven by TI EZ430-RF2500 boards scanning a typical 800 sqft apartment. Bumblebee radars are calibrated to detect the falling of human body, and the two-tier tracking algorithm is used on the ultrasonic sensors to track the location of the elderly people

Normalized Vector Codes for Object Recognition Using Artificial Neural Networks in the Framework of Picture Description Languages

Your Understanding how biological visual systems recognize objects is one of the ultimate goals in computational neuroscience. People are able to recognize different types of objects despite the fact that the objects may vary in view, points, sizes, scale, texture or even when they are translated or rotated. In this paper we focus on syntactic approach for the description of objects as Normalized Vector Codes using which objects are recognized based on their shapes

Leveraging Language to Learn Program Abstractions and Search Heuristics

Inductive program synthesis, or inferring programs from examples of desired behavior, offers a general paradigm for building interpretable, robust, and generalizable machine learning systems. Effective program synthesis depends on two key ingredients: a strong library of functions from which to build programs, and an efficient search strategy for finding programs that solve a given task. We introduce LAPS (Language for Abstraction and Program Search), a technique for using natural language annotations to guide joint learning of libraries and neurally-guided search models for synthesis. When integrated into a state-of-the-art library learning system (DreamCoder), LAPS produces higher-quality libraries and improves search efficiency and generalization on three domains -- string editing, image composition, and abstract reasoning about scenes -- even when no natural language hints are available at test time.Comment: appeared in Thirty-eighth International Conference on Machine Learning (ICML 2021

Data Science and Knowledge Discovery

Data Science (DS) is gaining significant importance in the decision process due to a mix of various areas, including Computer Science, Machine Learning, Math and Statistics, domain/business knowledge, software development, and traditional research. In the business field, DS's application allows using scientific methods, processes, algorithms, and systems to extract knowledge and insights from structured and unstructured data to support the decision process. After collecting the data, it is crucial to discover the knowledge. In this step, Knowledge Discovery (KD) tasks are used to create knowledge from structured and unstructured sources (e.g., text, data, and images). The output needs to be in a readable and interpretable format. It must represent knowledge in a manner that facilitates inferencing. KD is applied in several areas, such as education, health, accounting, energy, and public administration. This book includes fourteen excellent articles which discuss this trending topic and present innovative solutions to show the importance of Data Science and Knowledge Discovery to researchers, managers, industry, society, and other communities. The chapters address several topics like Data mining, Deep Learning, Data Visualization and Analytics, Semantic data, Geospatial and Spatio-Temporal Data, Data Augmentation and Text Mining

ChemVA: Interactive visual analysis of chemical compound similarity in virtual screening

In the modern drug discovery process, medicinal chemists deal with the complexity of analysis of large ensembles of candidate molecules. Computational tools, such as dimensionality reduction (DR) and classification, are commonly used to efficiently process the multidimensional space of features. These underlying calculations often hinder interpretability of results and prevent experts from assessing the impact of individual molecular features on the resulting representations. To provide a solution for scrutinizing such complex data, we introduce ChemVA, an interactive application for the visual exploration of large molecular ensembles and their features. Our tool consists of multiple coordinated views: Hexagonal view, Detail view, 3D view, Table view, and a newly proposed Difference view designed for the comparison of DR projections. These views display DR projections combined with biological activity, selected molecular features, and confidence scores for each of these projections. This conjunction of views allows the user to drill down through the dataset and to efficiently select candidate compounds. Our approach was evaluated on two case studies of finding structurally similar ligands with similar binding affinity to a target protein, as well as on an external qualitative evaluation. The results suggest that our system allows effective visual inspection and comparison of different high-dimensional molecular representations. Furthermore, ChemVA assists in the identification of candidate compounds while providing information on the certainty behind different molecular representations.Fil: Sabando, María Virginia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Ciencias e Ingeniería de la Computación. Universidad Nacional del Sur. Departamento de Ciencias e Ingeniería de la Computación. Instituto de Ciencias e Ingeniería de la Computación; ArgentinaFil: Ulbrich, Pavol. Masaryk University. Faculty of Sciences; República ChecaFil: Selzer, Matias Nicolas. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Ciencias e Ingeniería de la Computación. Universidad Nacional del Sur. Departamento de Ciencias e Ingeniería de la Computación. Instituto de Ciencias e Ingeniería de la Computación; Argentina. Universidad Nacional del Sur. Departamento de Ciencias e Ingeniería de la Computación. Laboratorio de Ciencias de la Imágenes; ArgentinaFil: Byska, Jan. Masaryk University. Faculty of Sciences; República ChecaFil: Mican, Jan. Masaryk University. Faculty of Sciences; República ChecaFil: Ponzoni, Ignacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Ciencias e Ingeniería de la Computación. Universidad Nacional del Sur. Departamento de Ciencias e Ingeniería de la Computación. Instituto de Ciencias e Ingeniería de la Computación; ArgentinaFil: Soto, Axel Juan. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Ciencias e Ingeniería de la Computación. Universidad Nacional del Sur. Departamento de Ciencias e Ingeniería de la Computación. Instituto de Ciencias e Ingeniería de la Computación; ArgentinaFil: Ganuza, María Luján. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Ciencias e Ingeniería de la Computación. Universidad Nacional del Sur. Departamento de Ciencias e Ingeniería de la Computación. Instituto de Ciencias e Ingeniería de la Computación; Argentina. Universidad Nacional del Sur. Departamento de Ciencias e Ingeniería de la Computación. Laboratorio de Ciencias de la Imágenes; ArgentinaFil: Kozlikova, Barbora. Masaryk University. Faculty of Sciences; República Chec

Joint Path planning and Power Allocation of a Cellular-Connected UAV using Apprenticeship Learning via Deep Inverse Reinforcement Learning

This paper investigates an interference-aware joint path planning and power allocation mechanism for a cellular-connected unmanned aerial vehicle (UAV) in a sparse suburban environment. The UAV's goal is to fly from an initial point and reach a destination point by moving along the cells to guarantee the required quality of service (QoS). In particular, the UAV aims to maximize its uplink throughput and minimize the level of interference to the ground user equipment (UEs) connected to the neighbor cellular BSs, considering the shortest path and flight resource limitation. Expert knowledge is used to experience the scenario and define the desired behavior for the sake of the agent (i.e., UAV) training. To solve the problem, an apprenticeship learning method is utilized via inverse reinforcement learning (IRL) based on both Q-learning and deep reinforcement learning (DRL). The performance of this method is compared to learning from a demonstration technique called behavioral cloning (BC) using a supervised learning approach. Simulation and numerical results show that the proposed approach can achieve expert-level performance. We also demonstrate that, unlike the BC technique, the performance of our proposed approach does not degrade in unseen situations