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Cumulative Difference Learning VAE for Time-Series with Temporally Correlated Inflow-Outflow
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Proposes DT-VAE, a VAE that models time series as cumulative differences from the initial value (driven by latent inflow/outflow), to mitigate error accumulation in time-series generation, plus a DTW-clustering-based DTP metric and new COVID-19 hospitalization datasets.
Problem
Autoregressive/step-wise time-series generators accumulate errors over time, and general-purpose generators ignore the inflow/outflow structure of quantities like hospital census, which is often unobserved.
Approach
Reformulate generation as learning the cumulative difference between the observation at time t and the initial value X0 (driven by latent inflow/outflow), so that each decoded step depends only on latent variables rather than recursively on prior generated values; implemented as a recurrent VAE (DT-VAE) with an optional VAE-GAN variant.
Key results
- DT-VAE-GAN achieves the best DTP score in most trend groups, e.g., County-DH INC 0.3717 vs 0.4164 for T-VAE-GAN and 0.4942 for TimeGAN, with reported average improvements of about 12% and up to 30%.
- On long-term prediction (first 40 steps predicting next 9), DT-VAE and DT-VAE-GAN achieve on average about 30% lower MSE than benchmarks and up to 65% lower, e.g., Traffic DEC MSE 0.0027 (DT-VAE) vs 0.0058 (PSA-GAN).
- DT-VAE and DT-VAE-GAN outperform TimeGAN, PSA-GAN, T-VAE and T-VAE-GAN on most DTP and prediction benchmarks, though TimeGAN and PSA-GAN are better on some trends (e.g., Stock INC for TimeGAN is worse; DT-VAE is worse than TimeGAN on Energy INC and County-DH INC).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use cumulative-difference learning with DT-VAE-GAN instead of the strongest listed baseline | Time-series generation · County-DH (INC, FLV, DEC) | DTP score: 0.4164±0.00054 -> 0.3717±0.00017; 0.8186±0.000362 -> 0.7636±0.00008; 0.9469±0.00012 -> 0.3271±0.00003 | Helped |
| Use cumulative-difference learning with DT-VAE-GAN instead of the strongest listed baseline | Time-series generation · County-DH (LTP) | DTP score: 0.4954±0.00001 -> 0.5225±0.00002 | Hurt |
| Use cumulative-difference learning with DT-VAE-GAN instead of the strongest listed baseline | Time-series generation · States-DH (INC, ERP, DEC, LTP) | DTP score: 0.3252±0.00124 -> 0.3240±0.00029; 0.8067±0.11438 -> 0.7564±0.00191; 0.4392±0.00066 -> 0.3135±0.00003; 0.7095±0.02287 -> | Helped |
| Use cumulative-difference learning with DT-VAE-GAN instead of the strongest listed baseline | Time-series generation · Energy (INC, DEC) | DTP score: 0.2286±0.00001 -> 0.3897±0.00059; 0.3780±0.00002 -> 0.2366±0.00068 | Mixed |
| Use cumulative-difference learning with DT-VAE-GAN instead of the strongest listed baseline | Time-series generation · Traffic (INC, DEC) | DTP score: 0.2153±0.00000 -> 0.2119±0.00000; 0.7286±0.00006 -> 0.3707±0.00003 | Helped |
| Use cumulative-difference learning with DT-VAE-GAN instead of the strongest listed baseline | Time-series generation · Stock (INC, DEC) | DTP score: 0.3066±0.00396 -> 0.2601±0.00022; 0.4796 ± 0.01595 -> 0.2860±0.00023 | Helped |
| Add the GAN component to DT-VAE (ablation) | Time-series generation · County-DH INC | DTP score: 0.8115±0.00055 -> 0.3717±0.00017 | Helped |
| Add the GAN component to DT-VAE (ablation) | Time-series generation · States-DH DEC | DTP score: 0.3178±0.00002 -> 0.3135±0.00003 | No clear effect |
Surprising findings
- DT-VAE alone (without the GAN) is worse than TimeGAN on several trends, e.g., County-DH INC DTP 0.8115 vs TimeGAN 0.4942, indicating the GAN component is important for some datasets.
Limitations
- Theoretical framework assumes inflow/outflow structure; interpretability and benefits may be reduced for domains without such structure (authors note the stock case lacks it).
- DT-VAE without the GAN underperforms on some trends and datasets.
- Experiments reduce cluster count for prediction tasks to get enough samples, which limits the evaluation setting.
Experimental setup
Datasets: Semi-synthetic hospital census (CIR-simulated arrivals) COVID-19 County Daily Hospitalization (CA, NY, PA) COVID-19 States Daily Hospitalization Solar Energy (Lai et al. 2018) Traffic (Cuturi 2011) Google stock data
Benchmarks: County-DH States-DH Energy Traffic Stock
Metrics: DTP score (DTW distance between DBA cluster centroids) long-term prediction MSE (TSTR with LSTM) t-SNE visualization mean and confidence interval visualization
Baselines: TimeGAN PSA-GAN T-VAE T-VAE-GAN AR model TimeVAE
Builds on: VAE VAE-GAN TimeGAN PSA-GAN
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