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world:std2025_abstract
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world:std2025_abstract [2025/11/14 14:37] rdouc |
world:std2025_abstract [2025/11/21 17:07] (current) rdouc |
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| <note round 80%> | <note round 80%> | ||
| * **Schedule**: 10H50-11H40 | * **Schedule**: 10H50-11H40 | ||
| - | * **Title**: to be completed. | + | * **Title**: Recursive learning of asymptotic variational objectives |
| </note> | </note> | ||
| + | * **Abstract**: General state-space models (SSMs) are widely used in statistical machine learning and are among the most classical generative models for sequential time-series data. SSMs, comprising latent Markovian states, can be subjected to variational inference (VI), but standard VI methods like the importance-weighted autoencoder (IWAE) lack functionality for streaming data. To enable online VI in SSMs when the observations are received in real time, we propose maximising an IWAE-type variational lower bound on the asymptotic contrast function, rather than the standard IWAE ELBO, using stochastic approximation. Unlike the recursive maximum likelihood method, which directly maximises the asymptotic contrast, our approach, called online sequential IWAE (OSI-WAE), allows for online learning of both model parameters and a Markovian recognition model for inferring latent states. By approximating filter state posteriors and their derivatives using sequential Monte Carlo (SMC) methods, we create a particle-based framework for online VI in SSMs. This approach is more theoretically well-founded than recently proposed online variational SMC methods. We provide rigorous theoretical results on the learning objective and a numerical study demonstrating the method’s efficiency in learning model parameters and particle proposal kernels. | ||
| </hidden> | </hidden> | ||
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| * **Joint work** | * **Joint work** | ||
| </note> | </note> | ||
| + | * **Abstract**: Sequential Monte Carlo (SMC) methods are general iterative stochastic algorithms to generate samples from a sequence of probability distributions. They proceed by recursively moving samples through the bridge via three crucial steps: importance sampling, resampling, and rejuvenating. The last step usually consists in running independent Markov chains, and only keeping the final states for the next iterations. | ||
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| + | Waste-free SMC [Dau and Chopin, 2022] avoids discarding the intermediary samples. | ||
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| + | We establish a finite-sample complexity bound for waste-free SMC, our proof generalises the approach of Marion et al [2023]. This bound prescribes sufficient conditions on the size of the particle system for the sampler to return estimated expectations $\hat{\pi}_T(f)$ such that $|\hat{\pi}_T − \pi_T(f)| ≤ \varepsilon$ with probability at least $1 − \eta$, for any bounded test function $f$. | ||
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| + | We demonstrate that waste-free SMC enjoys lower complexity than SMC differing from a logarithmic factor $O(\log(T\eta^{-1} \varepsilon^{-2}))$. | ||
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| + | We show that our analysis allows practitioners to tune the particle budget according to the specific statistical objective in hand. In particular, when the goal is to control errors for expectation estimates under $\hat{\pi}_T$ of bounded functions, the sampler can be run with an intentionally reduced number of particles in earlier iterations while still preserving finite-sample guarantees on the estimates. In doing so, we highlight an important distinction between those two objectives: estimating normalisation constants is more challenging than estimating expectations of bounded functions. | ||
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| </hidden> | </hidden> | ||
world/std2025_abstract.1763127433.txt.gz · Last modified: 2025/11/14 14:37 by rdouc
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