time series


Exploiting statistical dependencies of time series with hierarchical correlation reconstruction

arXiv.org Machine Learning

While we are usually focused on predicting future values of time series, it is often valuable to additionally predict their entire probability distributions, for example to evaluate risk or Monte Carlo simulations. On example of time series of $\approx$ 30000 Dow Jones Industrial Averages, there will be shown application of hierarchical correlation reconstruction for this purpose: mean-square fitting polynomial as joint density for (current value, context), where context is for example a few previous values. Then substituting the currently observed context and normalizing density to 1, we get predicted probability distribution for the current value. In contrast to standard machine learning approaches like neural networks, optimal coefficients here can be inexpensively directly calculated, are unique and independent, each has a specific cumulant-like interpretation, and such approximation can approach complete description of any joint distribution - providing a perfect tool to quantitatively describe and exploit statistical dependencies in time series.


Recurrent Auto-Encoder Model for Large-Scale Industrial Sensor Signal Analysis

arXiv.org Machine Learning

Recurrent auto-encoder model summarises sequential data through an encoder structure into a fixed-length vector and then reconstructs the original sequence through the decoder structure. The summarised vector can be used to represent time series features. In this paper, we propose relaxing the dimensionality of the decoder output so that it performs partial reconstruction. The fixed-length vector therefore represents features in the selected dimensions only. In addition, we propose using rolling fixed window approach to generate training samples from unbounded time series data. The change of time series features over time can be summarised as a smooth trajectory path. The fixed-length vectors are further analysed using additional visualisation and unsupervised clustering techniques. The proposed method can be applied in large-scale industrial processes for sensors signal analysis purpose, where clusters of the vector representations can reflect the operating states of the industrial system.


Time Series Deep Learning, Part 2: Predicting Sunspot Frequency with Keras LSTM In R

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Time Series Forecasting is a key area that can lead to Return On Investment (ROI) in a business. Think about this: A 10% improvement in forecast accuracy can save an organization millions of dollars.


Amazon.com: Introduction to Time Series and Forecasting (Springer Texts in Statistics) (9783319298528): Peter J. Brockwell, Richard A. Davis: Books

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This book is aimed at the reader who wishes to gain a working knowledge of time series and forecasting methods as applied to economics, engineering and the natural and social sciences. It assumes knowledge only of basic calculus, matrix algebra and elementary statistics. This third edition contains detailed instructions for the use of the professional version of the Windows-based computer package ITSM2000, now available as a free download from the Springer Extras website. The logic and tools of time series model-building are developed in detail. Numerous exercises are included and the software can be used to analyze and forecast data sets of the user's own choosing.


Data Science Predicting The Future

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Predictive analytics in data science rest on the shoulders of explanatory data analysis, which is precisely what we were discussing in our previous article – The What, Where and How of Data for Data Science. We talked about data in data science, and how business intelligence (BI) analysts use it to explain the past. In fact, everything is connected. Once the BI reports and dashboards have been prepared and insights – extracted from them – this information becomes the basis for predicting future values. And the accuracy of these predictions lies in the methods used.


Understanding Software System Behavior With ML and Time Series Data

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David Andrzejewski is an Engineering Manager at Sumo Logic and co-organizer of the SF Bay Area Machine Learning meetup group. Prior to Sumo Logic, David held a postdoctoral research position working on knowledge discovery at Lawrence Livermore National Laboratory (LLNL). QCon.ai is a AI and Machine Learning conference held in San Francisco for developers, architects & technical managers focused on applied AI/ML.


Change Point Detection in Time Series with R and Tableau

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This article was posted by Roberto Rösler on his personal blog about R and data mining. Roberto is a data scientist working at a major telecommunication company in Germany. Even if you still fight with the aftereffects of your new year's party, the following is something that may help in getting you more active because that's it what this blog post is about - Activity. Regardless of the business you are working in, I bet that customer activity is something that matters. An active customer typically is someone who is receptive for offers, whereas non-activity is a good indication for increasing churn probability or simply for a deteriorating customer relationship.


Build your first predictive model in seconds with InfluxDB and Loud ML

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In this webinar, Sébastien Leger from Loud ML will share with you the power of using unsupervised learning frameworks to gain deep insights into your InfluxData time series data (application and performance metrics, network flows, and financial or transactional data). He will then show you how to configure, model, and dig into the modeled times series data using the Loud ML API and your existing InfluxDB databases. This will open the recording. Here is an unedited transcript of the webinar "How to Build Your First Predictive Model in Seconds with InfluxDB and Loud ML" This is provided for those who prefer to read than watch the webinar. Please note that the transcript is raw. We apologize for any transcribing errors. We have a really great webinar today. We actually always have a great webinar. But today, I'm really excited. We'll get started in just one minute. In the meantime, I'll just cover some housekeeping items. If you have any questions during the presentation, please feel free to type them in either the Q&A, or the Chat Panel. And if you really, really, really want to speak out your questions, just raise your hand and I can un-mute you and you can talk to Sebastian directly. In addition, as always, I will--this session's being recorded. After I do the edit, then I'll post it and you will get--usually you'll get the email first thing tomorrow morning. But I usually end up posting this in a couple of hours. So if you go back to the link, you'll see that the page actually will change from the registration page to the recording. So you'll be able to take a listen to it again. And also, we have trainings on Thursdays.


Deep Self-Organization: Interpretable Discrete Representation Learning on Time Series

arXiv.org Machine Learning

Human professionals are often required to make decisions based on complex multivariate time series measurements in an online setting, e.g. in health care. Since human cognition is not optimized to work well in high-dimensional spaces, these decisions benefit from interpretable low-dimensional representations. However, many representation learning algorithms for time series data are difficult to interpret. This is due to non-intuitive mappings from data features to salient properties of the representation and non-smoothness over time. To address this problem, we propose to couple a variational autoencoder to a discrete latent space and introduce a topological structure through the use of self-organizing maps. This allows us to learn discrete representations of time series, which give rise to smooth and interpretable embeddings with superior clustering performance. Furthermore, to allow for a probabilistic interpretation of our method, we integrate a Markov model in the latent space. This model uncovers the temporal transition structure, improves clustering performance even further and provides additional explanatory insights as well as a natural representation of uncertainty. We evaluate our model on static (Fashion-)MNIST data, a time series of linearly interpolated (Fashion-)MNIST images, a chaotic Lorenz attractor system with two macro states, as well as on a challenging real world medical time series application. In the latter experiment, our representation uncovers meaningful structure in the acute physiological state of a patient.


EigenNetworks

arXiv.org Machine Learning

In many applications, the interdependencies among a set of $N$ time series $\{ x_{nk}, k>0 \}_{n=1}^{N}$ are well captured by a graph or network $G$. The network itself may change over time as well (i.e., as $G_k$). We expect the network changes to be at a much slower rate than that of the time series. This paper introduces eigennetworks, networks that are building blocks to compose the actual networks $G_k$ capturing the dependencies among the time series. These eigennetworks can be estimated by first learning the time series of graphs $G_k$ from the data, followed by a Principal Network Analysis procedure. Algorithms for learning both the original time series of graphs and the eigennetworks are presented and discussed. Experiments on simulated and real time series data demonstrate the performance of the learning and the interpretation of the eigennetworks.