**Time Series Database (TSDB)**

A time series database (TSDB) is a software system that is optimized for handling time series data, arrays of numbers indexed by time (a datetime or a datetime range). In some fields these time series are called profiles, curves, or traces. A time series of stock prices might be called a price curve. A time series of energy consumption might be called a load profile. A log of temperature values over time might be called a temperature trace. Despite the disparate names, many of the same mathematical operations, queries, or database transactions are useful for analysing all of them. The implementation of a database that can correctly, reliably, and efficiently implement these operations must be specialized for time-series data. TSDBs are databases that are optimized for time series data. Software with complex logic or business rules and high transaction volume for time series data may not be practical with traditional relational database management systems. Flat file databases are not a viable option either, if the data and transaction volume reaches a maximum threshold determined by the capacity of individual servers (processing power and storage capacity). Queries for historical data, replete with time ranges and roll ups and arbitrary time zone conversions are difficult in a relational database. Compositions of those rules are even more difficult. This is a problem compounded by the free nature of relational systems themselves. Many relational systems are often not modelled correctly with respect to time series data. TSDBs on the other hand impose a model and this allows them to provide more features for doing so. Ideally, these repositories are often natively implemented using specialized database algorithms. However, it is possible to store time series as binary large objects (BLOBs) in a relational database or by using a VLDB approach coupled with a pure star schema. Efficiency is often improved if time is treated as a discrete quantity rather than as a continuous mathematical dimension. Database joins across multiple time series data sets is only practical when the time tag associated with each data entry spans the same set of discrete times for all data sets across which the join is performed. … **Intelligence Graph**

In fact, there exist three genres of intelligence architectures: logics (e.g. \textit{Random Forest, A$^*$ Searching}), neurons (e.g. \textit{CNN, LSTM}) and probabilities (e.g. \textit{Naive Bayes, HMM}), all of which are incompatible to each other. However, to construct powerful intelligence systems with various methods, we propose the intelligence graph (short as \textbf{\textit{iGraph}}), which is composed by both of neural and probabilistic graph, under the framework of forward-backward propagation. By the paradigm of iGraph, we design a recommendation model with semantic principle. First, the probabilistic distributions of categories are generated from the embedding representations of users/items, in the manner of neurons. Second, the probabilistic graph infers the distributions of features, in the manner of probabilities. Last, for the recommendation diversity, we perform an expectation computation then conduct a logic judgment, in the manner of logics. Experimentally, we beat the state-of-the-art baselines and verify our conclusions. … **Physics-Informed Kriging (PhIK)**

In this work, we propose a new Gaussian process regression (GPR) method: physics-informed Kriging (PhIK). In the standard data-driven Kriging, the unknown function of interest is usually treated as a Gaussian process with assumed stationary covariance with hyperparameters estimated from data. In PhIK, we compute the mean and covariance function from realizations of available stochastic models, e.g., from realizations of governing stochastic partial differential equations solutions. Such a constructed Gaussian process generally is non-stationary, and does not assume a specific form of the covariance function. Our approach avoids the costly optimization step in data-driven GPR methods to identify the hyperparameters. More importantly, we prove that the physical constraints in the form of a deterministic linear operator are guaranteed in the resulting prediction. We also provide an error estimate in preserving the physical constraints when errors are included in the stochastic model realizations. To reduce the computational cost of obtaining stochastic model realizations, we propose a multilevel Monte Carlo estimate of the mean and covariance functions. Further, we present an active learning algorithm that guides the selection of additional observation locations. The efficiency and accuracy of PhIK are demonstrated for reconstructing a partially known modified Branin function and learning a conservative tracer distribution from sparse concentration measurements. … **Neural Network Synthesis Tool (NeST)**

Neural networks (NNs) have begun to have a pervasive impact on various applications of machine learning. However, the problem of finding an optimal NN architecture for large applications has remained open for several decades. Conventional approaches search for the optimal NN architecture through extensive trial-and-error. Such a procedure is quite inefficient. In addition, the generated NN architectures incur substantial redundancy. To address these problems, we propose an NN synthesis tool (NeST) that automatically generates very compact architectures for a given dataset. NeST starts with a seed NN architecture. It iteratively tunes the architecture with gradient-based growth and magnitude-based pruning of neurons and connections. Our experimental results show that NeST yields accurate yet very compact NNs with a wide range of seed architecture selection. For example, for the LeNet-300-100 (LeNet-5) NN architecture derived from the MNIST dataset, we reduce network parameters by 34.1x (74.3x) and floating-point operations (FLOPs) by 35.8x (43.7x). For the AlexNet NN architecture derived from the ImageNet dataset, we reduce network parameters by 15.7x and FLOPs by 4.6x. All these results are the current state-of-the-art for these architectures. …

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