More than twenty years after its introduction, Annealed Importance Sampling (AIS) remains one of the most effective methods for marginal likelihood estimation.

Sampling from a complex distributionπ and approximating its intractable normalizing constantZ are challenging problems.

More than twenty years after its introduction, Annealed Importance Sampling (AIS) remains one of the most effective methods for marginal likelihood estimation.

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 (OSIWAE), 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.

Differentiable particle filters combine the flexibility of neural networks with the probabilistic nature of sequential Monte Carlo methods. However, traditional approaches rely on the availability of labelled data, i.e., the ground truth latent state information, which is often difficult to obtain in real-world applications. This paper compares the effectiveness of two semi-supervised training objectives for differentiable particle filters. We present results in two simulated environments where labelled data are scarce.

The expectation maximization (EM) algorithm is a widespread method for empirical Bayesian inference, but its expectation step (E-step) is often intractable. Employing a stochastic approximation scheme with Markov chain Monte Carlo (MCMC) can circumvent this issue, resulting in an algorithm known as MCMC-SAEM. While theoretical guarantees for MCMC-SAEM have previously been established, these results are restricted to the case where asymptotically unbiased MCMC algorithms are used. In practice, MCMC-SAEM is often run with asymptotically biased MCMC, for which the consequences are theoretically less understood. In this work, we fill this gap by analyzing the asymptotics and non-asymptotics of SAEM with biased MCMC steps, particularly the effect of bias. We also provide numerical experiments comparing the Metropolis-adjusted Langevin algorithm (MALA), which is asymptotically unbiased, and the unadjusted Langevin algorithm (ULA), which is asymptotically biased, on synthetic and real datasets. Experimental results show that ULA is more stable with respect to the choice of Langevin stepsize and can sometimes result in faster convergence.

We show that taking the width and depth to infinity in a deep neural network with skip connections, when branches are scaled by $1/\sqrt{depth}$ (the only nontrivial scaling), result in the same covariance structure no matter how that limit is taken. This explains why the standard infinite-width-then-depth approach provides practical insights even for networks with depth of the same order as width. We also demonstrate that the pre-activations, in this case, have Gaussian distributions which has direct applications in Bayesian deep learning. We conduct extensive simulations that show an excellent match with our theoretical findings.

OpenAI CEO Sam Altman believes AI can help usher in "unbelievable abundance," but he says he wants to ensure that such abundance is shared. Toward that end, Altman has embraced a theory of 19th century political economist Henry George, who in his own lifetime worried about wealth amassing in the hands of the few following the Industrial Revolution. George posited that greater equality could be enjoyed if the economic value of land belonged equally to all members of society. Altman similarly believes that in a world where jobs may create less economic value, a land tax could make up for income tax and guarantee that all individuals' assets rise as land -- a fixed asset -- grows in value. He's putting his money where his mouth is, too, leading a seed round in a six-month-old startup that represents a step in that same direction.

Particle smoothers are SMC (Sequential Monte Carlo) algorithms designed to approximate the joint distribution of the states given observations from a state-space model. We propose dSMC (de-Sequentialized Monte Carlo), a new particle smoother that is able to process $T$ observations in $\mathcal{O}(\log T)$ time on parallel architecture. This compares favourably with standard particle smoothers, the complexity of which is linear in $T$. We derive $\mathcal{L}_p$ convergence results for dSMC, with an explicit upper bound, polynomial in $T$. We then discuss how to reduce the variance of the smoothing estimates computed by dSMC by (i) designing good proposal distributions for sampling the particles at the initialization of the algorithm, as well as by (ii) using lazy resampling to increase the number of particles used in dSMC. Finally, we design a particle Gibbs sampler based on dSMC, which is able to perform parameter inference in a state-space model at a $\mathcal{O}(\log(T))$ cost on parallel hardware.

Sure, Spider-Man: Miles Morales and the Dark Souls remake are getting most of the PlayStation 5 love, but Sony's most significant next-generation launch game may be Astro's Playroom. It's a showpiece for the new DualSense controller's haptic capabilities, which includes finely tuned rumbling and adaptive triggers with adjustable tension. Best of all, you can start playing it on your PS5 right away; it's pre-installed on every system. Just like with Astro Bot Rescue Mission on the PlayStation VR, the diminutive robot is the ideal guide as Sony breaks new ground with hardware. As I mentioned in my PlayStation 5 review, simply booting up the game jolted me awake -- it vibrated in my hands as if it was the one holding me.