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Probabilistic Forecasting of Irregularly Sampled Time Series with Missing Values via Conditional Normalizing Flows
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Proposes ProFITi, a conditional normalizing flow that learns joint conditional distributions of future values of irregularly sampled multivariate time series with missing values, using a sorted invertible triangular attention layer and the Shiesh activation.
Problem
Probabilistic forecasting of irregularly sampled multivariate time series with missing values, where existing models only estimate marginal Gaussian distributions per channel and timepoint rather than joint distributions.
Approach
Conditional normalizing flow whose blocks use a sorted invertible triangular attention (SITA) layer, conditioned on a GraFITi encoder of observations and queries, plus Shiesh, a new invertible activation covering the whole real line with analytic inverse and gradient, enabling permutation-invariant joint density estimation over a variable number of queried targets.
Key results
- ProFITi achieves njNLL of -3.226 on USHCN, -0.647 on Physionet'12, -0.377 on MIMIC-III and -1.777 on MIMIC-IV, outperforming all baselines.
- ProFITi gives an average log-likelihood gain of 2.0 over the next-best model GraFITi+.
- Ablation on Physionet'12 shows removing Shiesh raises njNLL from -0.647 to 0.285, and removing SITA gives -0.470.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use ProFITi instead of GraFITi+ | Probabilistic forecasting model · USHCN | njNLL: 0.489±0.173 -> -3.226±0.225 | Helped |
| Use ProFITi instead of GraFITi+ | Probabilistic forecasting model · Physionet’12 | njNLL: 0.367±0.021 -> -0.647±0.078 | Helped |
| Use ProFITi instead of GraFITi+ | Probabilistic forecasting model · MIMIC-III | njNLL: 0.721±0.053 -> -0.377±0.032 | Helped |
| Use ProFITi instead of GraFITi+ | Probabilistic forecasting model · MIMIC-IV | njNLL: 0.287±0.040 -> -1.777±0.066 | Helped |
| Add SITA (ablation) | ProFITi · Physionet’12 | njNLL: -0.470±0.017 -> -0.647±0.078 | Helped |
| Add Shiesh (ablation) | ProFITi · Physionet’12 | njNLL: 0.285±0.061 -> -0.647±0.078 | Helped |
| Remove SITA and Shiesh (ablation) | ProFITi · Physionet’12 | njNLL: -0.647±0.078 -> 0.372±0.021 | Hurt |
| Replace Shiesh with PReLU (ablation) | ProFITi · Physionet’12 | njNLL: -0.647±0.078 -> 0.384±0.060 | Hurt |
| Replace Shiesh with Leaky-ReLU (ablation) | ProFITi · Physionet’12 | njNLL | Hurt |
| Replace Atri with AiTrans (ablation) | ProFITi · Physionet’12 | njNLL: -0.647±0.078 -> -0.199±0.141 | Hurt |
| Replace Atri with Areg (ablation) | ProFITi · Physionet’12 | njNLL: -0.647±0.078 -> -0.778±0.016 | Helped |
Surprising findings
- The AiTrans invertible attention variant performs poorly due to its restriction to positive covariances.
- GraFITi+ (point-forecast encoder with Gaussian head) gives lower MSE than ProFITi marg, despite ProFITi's better likelihoods.
Limitations
- ProFITi requires sampling to compute MSE and CRPS, and its point forecasts are less accurate than GraFITi.
- Full dense attention (Areg) has cubic determinant cost and does not scale; the triangular variant is used instead.
- Shiesh parameter b fixed to 1 in experiments.
Experimental setup
Datasets: MIMIC-III MIMIC-IV Physionet'12 USHCN
Benchmarks: Physionet'12 MIMIC-III MIMIC-IV USHCN
Metrics: normalized joint negative log-likelihood marginal negative log-likelihood CRPS MSE
Baselines: CRU Neural-Flows GRU-ODE-Bayes GraFITi+ HETVAE Multi-task GPR
Builds on: GraFITi Neural Flows unconstrained monotonic neural networks Invertible Attention
Closest papers by meaning
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