ML+X Forum: Time-Series Analysis

Join the ML+X community on Tuesday, Oct. 10, 12-1pm, an exciting forum dedicated to the world of time-series analysis, including methods for comparing and modeling sequence data. We will explore both statistical and machine learning methods for understanding temporal patterns and trends. See the speaker lineup below for details, and please register (lunch provided) by 5pm on Friday (10/6) if you plan to attend in-person!

1. Computational Methods for Comparative Time Clocks in Early Development and Tissue Regeneration, Peng Jiang
   Comparative time series transcriptome analysis is a powerful tool to study development, evolution, aging, disease progression and cancer prognosis. We develop TimeMeter, a statistical method and tool to assess temporal gene expression similarity, and identify differentially progressing genes where one pattern is more temporally advanced than the other. We apply TimeMeter to several datasets, and show that TimeMeter is capable of characterizing complicated temporal gene expression associations. Interestingly, we find: (i) the measurement of differential progression provides a novel feature in addition to pattern similarity that can characterize early developmental divergence between two species; (ii) genes exhibiting similar temporal patterns between human and mouse during neural differentiation are under strong negative (purifying) selection during evolution; (iii) analysis of genes with similar temporal patterns in mouse digit regeneration and axolotl blastema differentiation reveals common gene groups for appendage regeneration with potential implications in regenerative medicine. One challenge is how to evaluate this method. Because there is no grand-true about the “best time alignment method”. For AI/ML, the evaluation is very easy (e.g., K-fold cross-validation) but for comparative time-course data, how do we know what we calculate is right is a major challenge. The validation is hard. So we need to find alternative ways to demonstrate our methods make sense.
   
   
2. Controlled Differential Equations on Long Sequences via Non-standard Wavelets, Sourav Pal
   Neural Controlled Differential equations (NCDE) are a powerful mechanism to model the dynamics in temporal sequences, e.g., applications involving physiological measures, where apart from the initial condition, the dynamics also depend on subsequent measures or even a different "control" sequence. But NCDEs do not scale well to longer sequences. Existing strategies adapt rough path theory, and instead model the dynamics over summaries known as log signatures. While rigorous and elegant, invertibility of these summaries is difficult, and limits the scope of problems where these ideas can offer strong benefits (reconstruction, generative modeling). For tasks where it is sensible to assume that the (long) sequences in the training data are a fixed length of temporal measurements – this assumption holds in most experiments tackled in the literature – we describe an efficient simplification. First, we recast the regression/classification task as an integral transform. We then show how restricting the class of operators (permissible in the integral transform), allows the use of a known algorithm that leverages non-standard Wavelets to decompose the operator. Thereby, our task (learning the operator) radically simplifies. A neural variant of this idea yields consistent improvements across a wide gamut of use cases tackled in existing works. We also describe a novel application on modeling tasks involving coupled differential equations. Challenge: The model in it’s most general form is hard to train with small datasets, it is prone to overfitting. Hence, we introduce a regularization scheme based on the parameters of the model to help resolve this issue.
   

Finding the Orchard View room: The Orchard View room is located on the 3rd floor of Discovery Building — room 3280. To get to the third floor, take the elevator located next to the Aldo’s Cafe kitchen (see photo). If you cannot attend in-person, we invite you to stream the event via Zoom: https://uwmadison.zoom.us/j/92639425571?pwd=Z0tCaWZxK0dDcWs2dm51dXZpcy9mQT09