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Variational Bayesian filtering Factor Analysis (VBfFA) to estimate time-varying statistical factors of large set of multiple time-series
Overview
The variational Bayesian filtering factor analysis (VBfFA) algorithm/model is a filter with dimension-reduction, or rank-reduction, to extract a number of ever-evolving unobserved common factors, or signals from common sources, underlying and influencing a large number of related time-series.
Relevant examples of time-series include: economic indicators in a nation, region, or international economic sector; prices of assets in a national, regional or global marketplace; performance score time-series related to a business marketing campaign; and time-series signals from an array of radar or sonar sensors tracking several moving targets.
By applying (variational) Bayesian filtering (instead of traditional moving/rolling data windows for frequentist time-dependent analysis), the VBfFA algorithm is able to update predictions with only the newly arrived time-series data point (instead of all data points in the data window); and predict underlying changes in time-series early.
Highlights
- WHY Bayesian filter? To estimate a “time-varying” or “time-dependent” statistic of time-series, traditional method is to use “moving/rolling data window” and/or “exponentially decayed time weights”. A straightforward and natural alternative is to use Bayesian framework: at each moment in time, using the last estimate as prior; conditional distribution of estimate (given statistical model for the estimate) as likelihood; and newly arrived/available time-series data point as observation. Then, the resulted posterior is a new estimate. In time-domain, such a Bayesian formulation is a filter.
- WHY variational Bayes? The Bayesian filtering framework for estimating time-dependent statistics of time-series is straightforward and simple. The need of joint and conditional probability distribution functions, however, makes actual estimation complicated, difficult or even intractable. Discretized approximation, e.g. numerical particle filters, is computation-intensive and prone to cumulative errors in numerical distributions. A variational Bayes (VB) is an analytical approximation. After tedious derivation, a VB is fast, as long as the assumptions on distributions are appropriate.
- WHAT next? In addition to a stand-alone filtering package for time-varying factor analysis on multiple time-series, the VBfFA algorithm will be employed as the underlying factor analysis engine of other machine learning packages here introduced earlier by i4cast LLC: LMDFM (long memory dynamic factor model); YWpcAR (Yule-Walker-PCA autoregressive model); LMVAR (long memory vector autoregressive model); and CTVARF (continuously trained vector autoregressive forecast model). We will introduce a published general-purpose multivariate variational Bayesian filter (VBF) algorithm as well.
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Dimension | Description | Cost/host/hour |
|---|---|---|
ml.m5.xlarge Inference (Batch) Recommended | Model inference on the ml.m5.xlarge instance type, batch mode | $0.10 |
ml.m5.xlarge Inference (Real-Time) Recommended | Model inference on the ml.m5.xlarge instance type, real-time mode | $0.10 |
ml.m5.xlarge Training Recommended | Algorithm training on the ml.m5.xlarge instance type | $0.10 |
ml.m4.4xlarge Inference (Batch) | Model inference on the ml.m4.4xlarge instance type, batch mode | $0.10 |
ml.g4dn.4xlarge Inference (Batch) | Model inference on the ml.g4dn.4xlarge instance type, batch mode | $0.10 |
ml.m5.4xlarge Inference (Batch) | Model inference on the ml.m5.4xlarge instance type, batch mode | $0.10 |
ml.m4.16xlarge Inference (Batch) | Model inference on the ml.m4.16xlarge instance type, batch mode | $0.10 |
ml.p3.16xlarge Inference (Batch) | Model inference on the ml.p3.16xlarge instance type, batch mode | $0.10 |
ml.m5.2xlarge Inference (Batch) | Model inference on the ml.m5.2xlarge instance type, batch mode | $0.10 |
ml.g4dn.2xlarge Inference (Batch) | Model inference on the ml.g4dn.2xlarge instance type, batch mode | $0.10 |
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Version release notes
VBfFA algorithm is a factor analysis filter to extract a number of ever-evolving unobserved common factors, or signals from common sources, underlying and influencing a large number of related time-series data.
Current version of the VBfFA algorithm estimates: time-series of posterior from the (variational) Bayesian filtering; predicted values and time-dependent variances of common factors and time-dependent factor loadings; predicted time-dependent variance-covariance matrix of multiple time-series; and evaluation scores of the predicted time-series of variance-covariance matrix.
Additional details
Inputs
- Summary
The VBfFA algorithm takes, as input data, multiple time-series data contained in a CSV (comma separated value) data table, in a format of a CSV text-string or a CSV text-file.
Each row of the data table is for values of an individual time-series (TS). Row header is the label or symbol of the time-series. Each column is for values of all time-series at a specific moment in time. Column header is the time-index or time-stamp of the moment.
- Input MIME type
- text/csv
https://github.com/i4cast/aws/blob/main/variational_Bayesian_filtering_factor_analysis/input/Weekly_VTS_4Yr.csv
https://github.com/i4cast/aws/blob/main/variational_Bayesian_filtering_factor_analysis/input/Weekly_VTS_4Yr.csv
Input data descriptions
The following table describes supported input data fields for real-time inference and batch transform.
Field name | Description | Constraints | Required |
|---|---|---|---|
Values of time stamp | Each row of the data table is for values of an individual time-series (TS). Row header is the label or symbol of the time-series. Each column is for values of all time-series at a specific moment in time. Column header is the time-index or time-stamp of the moment. The first data column is for the earliest time and the last column for the most recent time. The current version of VBfFA requires equally spaced time-stamps. | Type: FreeText | Yes |
Support
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For questions or call-back number, please send email to i4cast LLC at prod.i4cast@gmail.com .
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