Linear-Gaussian Scalar Report Snapshot
Source artifact rendered for reading.
This committed snapshot mirrors the compact report generated by:
make aggregate-linear-gaussian-reports
Generated output remains under ignored outputs/ directories. This copy keeps
the scalar benchmark interpretation reviewable from a clean checkout without
rerunning the full sweeps.
Interpretation
- Frozen marginal is the key control: it preserves exact Kalman filtering while testing learned edge/backward conditionals.
- Self-fed supervised filtering is the strongest learned baseline.
- Vanilla MC ELBO is the true unsupervised baseline and remains under-dispersed in weak-observation and Q/R-mismatch regimes.
- Oracle-calibrated ELBO rows are diagnostics. Their variance penalties use oracle/reference filtering variance targets, so they should not be reported as fully unsupervised results.
- Direct non-residualized ELBO is much weaker in this scalar benchmark, so strong scalar results should be described as residualized/analytic-update filters rather than learned-from-scratch Bayesian filtering.
Weak Observability
| Pattern | Model | state NLL | cov 90 | var ratio | pred NLL |
|---|---|---|---|---|---|
| sinusoidal_reference | exact Kalman | 0.401983 | 0.900220 | 1.000000 | 0.600858 |
| sinusoidal_reference | frozen marginal backward MLP | 0.401983 | 0.900220 | 1.000006 | 0.600858 |
| sinusoidal_reference | self-fed supervised + oracle variance calibration | 0.415025 | 0.898189 | 1.013291 | 0.607679 |
| sinusoidal_reference | MC ELBO structured | 0.492098 | 0.849060 | 0.662955 | 0.622721 |
| sinusoidal_reference | oracle-variance-calibrated MC ELBO | 0.438505 | 0.893258 | 0.998726 | 0.615828 |
| weak_sinusoidal | exact Kalman | 1.175155 | 0.899137 | 1.000000 | 0.363894 |
| weak_sinusoidal | frozen marginal backward MLP | 1.175155 | 0.899137 | 1.000005 | 0.363894 |
| weak_sinusoidal | self-fed supervised + oracle variance calibration | 1.184098 | 0.896826 | 0.999368 | 0.366838 |
| weak_sinusoidal | MC ELBO structured | 1.291485 | 0.813155 | 0.668404 | 0.377645 |
| weak_sinusoidal | oracle-variance-calibrated MC ELBO | 1.216600 | 0.881791 | 0.967360 | 0.373358 |
| intermittent_sinusoidal | exact Kalman | 0.911865 | 0.899402 | 1.000000 | 0.431967 |
| intermittent_sinusoidal | frozen marginal backward MLP | 0.911865 | 0.899402 | 1.000005 | 0.431967 |
| intermittent_sinusoidal | self-fed supervised + oracle variance calibration | 0.912915 | 0.899064 | 1.002485 | 0.432007 |
| intermittent_sinusoidal | MC ELBO structured | 0.947600 | 0.865519 | 0.892053 | 0.435886 |
| intermittent_sinusoidal | oracle-variance-calibrated MC ELBO | 0.929798 | 0.892521 | 0.989241 | 0.433509 |
| zero_unobservable | exact Kalman | 2.740063 | 0.904118 | 1.000000 | 0.268452 |
| zero_unobservable | frozen marginal backward MLP | 2.740063 | 0.904118 | 1.000003 | 0.268452 |
| zero_unobservable | self-fed supervised + oracle variance calibration | 2.742646 | 0.911780 | 1.055466 | 0.268452 |
| zero_unobservable | MC ELBO structured | 7.010386 | 0.391683 | 0.108259 | 0.268452 |
| zero_unobservable | oracle-variance-calibrated MC ELBO | 2.740240 | 0.905575 | 1.004223 | 0.268452 |
| random_normal | exact Kalman | 0.218954 | 0.897559 | 1.000000 | 0.693509 |
| random_normal | frozen marginal backward MLP | 0.218954 | 0.897563 | 1.000013 | 0.693509 |
| random_normal | self-fed supervised + oracle variance calibration | 0.223558 | 0.896183 | 0.989436 | 0.694443 |
| random_normal | MC ELBO structured | 0.306598 | 0.847164 | 0.776662 | 0.711019 |
| random_normal | oracle-variance-calibrated MC ELBO | 0.272531 | 0.889945 | 0.972512 | 0.707264 |
Randomized Q/R
| eval Q | eval R | Model | state NLL | cov 90 | var ratio | pred NLL |
|---|---|---|---|---|---|---|
| 0.03 | 0.03 | frozen marginal backward MLP | -0.192878 | 0.900346 | 1.000011 | 0.004960 |
| 0.03 | 0.03 | regime-local self-fed supervised | -0.168295 | 0.895707 | 1.015044 | 0.018927 |
| 0.03 | 0.03 | oracle regime-variance-calibrated MC ELBO | -0.051062 | 0.861226 | 1.011369 | 0.069179 |
| 0.03 | 0.3 | frozen marginal backward MLP | 0.461248 | 0.899919 | 1.000011 | 0.941608 |
| 0.03 | 0.3 | regime-local self-fed supervised | 0.474714 | 0.900415 | 1.005023 | 0.947430 |
| 0.03 | 0.3 | oracle regime-variance-calibrated MC ELBO | 0.553383 | 0.849805 | 0.972514 | 0.965394 |
| 0.1 | 0.1 | frozen marginal backward MLP | 0.401983 | 0.900220 | 1.000006 | 0.600858 |
| 0.1 | 0.1 | regime-local self-fed supervised | 0.416249 | 0.894421 | 0.999319 | 0.607951 |
| 0.1 | 0.1 | oracle regime-variance-calibrated MC ELBO | 0.461048 | 0.880180 | 0.989530 | 0.625405 |
| 0.3 | 0.03 | frozen marginal backward MLP | 0.133134 | 0.900175 | 1.000005 | 0.530738 |
| 0.3 | 0.03 | regime-local self-fed supervised | 0.146506 | 0.894499 | 1.010729 | 0.536225 |
| 0.3 | 0.03 | oracle regime-variance-calibrated MC ELBO | 0.180429 | 0.903296 | 0.990049 | 0.546888 |
| 0.3 | 0.3 | frozen marginal backward MLP | 0.943551 | 0.900334 | 1.000003 | 1.144913 |
| 0.3 | 0.3 | regime-local self-fed supervised | 0.957915 | 0.892554 | 0.992193 | 1.150463 |
| 0.3 | 0.3 | oracle regime-variance-calibrated MC ELBO | 0.980429 | 0.894177 | 0.998269 | 1.157446 |
Next Milestone
Treat scalar linear-Gaussian as ready after the labeling cleanup. The next research milestone is nonlinear strict-filter ELBO versus the grid reference, not GRU/LSTM/Mamba expansion.