We consider the problem of localizing change points in high-dimensional linear regression. We propose an Approximate Message Passing (AMP) algorithm for estimating both the signals and the change point locations. Assuming Gaussian covariates, we give an exact asymptotic characterization of its estimation performance in the limit where the number of samples grows proportionally to the signal dimension. Our algorithm can be tailored to exploit any prior information on the signal, noise, and change points. It also enables uncertainty quantification in the form of an efficiently computable approximate posterior distribution, whose asymptotic form we characterize exactly. We validate our theory via numerical experiments, and demonstrate the favorable performance of our estimators on both synthetic data and images.

We study the problem of regression in a generalized linear model (GLM) with multiple signals and latent variables. This model, which we call a matrix GLM, covers many widely studied problems in statistical learning, including mixed linear regression, max-affine regression, and mixture-of-experts. In mixed linear regression, each observation comes from one of $L$ signal vectors (regressors), but we do not know which one; in max-affine regression, each observation comes from the maximum of $L$ affine functions, each defined via a different signal vector. The goal in all these problems is to estimate the signals, and possibly some of the latent variables, from the observations. We propose a novel approximate message passing (AMP) algorithm for estimation in a matrix GLM and rigorously characterize its performance in the high-dimensional limit. This characterization is in terms of a state evolution recursion, which allows us to precisely compute performance measures such as the asymptotic mean-squared error. The state evolution characterization can be used to tailor the AMP algorithm to take advantage of any structural information known about the signals. Using state evolution, we derive an optimal choice of AMP `denoising' functions that minimizes the estimation error in each iteration. The theoretical results are validated by numerical simulations for mixed linear regression, max-affine regression, and mixture-of-experts. For max-affine regression, we propose an algorithm that combines AMP with expectation-maximization to estimate intercepts of the model along with the signals. The numerical results show that AMP significantly outperforms other estimators for mixed linear regression and max-affine regression in most parameter regimes.

At its AI Day, Tesla unveiled its Dojo supercomputer technology while flexing its growing in-house chip design talent. The automaker claims to have developed the fastest AI training machine in the world. For years now, Tesla has been teasing the development of a new supercomputer in-house optimized for neural net video training. Tesla is handling an insane amount of video data from its fleet of over 1 million vehicles, which it uses to train its neural nets. The automaker found itself unsatisfied with current hardware options to train its computer vision neural nets and believed it could do better internally. Over the last two years, CEO Elon Musk has been teasing the development of Tesla's own supercomputer called "Dojo."

In April, at a special event at Tesla's Palo Alto, California headquarters called Tesla Autonomy Investor Day, Tesla CEO Elon Musk announced that Tesla vehicles are using a new custom-designed processor to power its Autopilot full self-driving (FSD) system. At the time Musk said that no chip was available that had the processing power and power constraints that Tesla required, so the automaker built its own from scratch. Now the technical details of the new chip have been revealed for the first time. At the Hot Chips conference in San Francisco on Tuesday, Tesla's VP of hardware engineering Pete Bannon revealed of the details of the chipset that will power Tesla's future Autopilot, full self-driving (FSD) system. Bannon said that the new AI-powered chip is 21 times faster that the Nvidia chip it's replacing and only 80% of the cost.

Tesla showed the computer at the Hot Chips conference. Designing your own chips is hard. But Tesla, one of the most aggressive developers of autonomous vehicle technology, thinks it's worth it. The company shared details Tuesday about how it fine-tuned the design of its AI chips so two of them are smart enough to power its cars' upcoming "full self-driving" abilities. Tesla Chief Executive Elon Musk and his colleagues revealed the company's third-generation computing hardware in April.

The decision to take vaccinations and other protective interventions for avoiding an infection is a natural game-theoretic setting. Most of the work on vaccination games has focused on decisions at the start of an epidemic. However, a lot of people defer their vaccination decisions, in practice. For example, in the case of the seasonal flu, vaccination rates gradually increase, as the epidemic rate increases. This motivates the study of temporal vaccination games, in which vaccination decisions can be made more than once. An important issue in the context of temporal decisions is that of resource limitations, which may arise due to production and distribution constraints. While there has been some work on temporal vaccination games, resource constraints have not been considered. In this paper, we study temporal vaccination games for epidemics in the SI (susceptible-infectious) model, with resource constraints in the form of a repeated game in complex social networks, with budgets on the number of vaccines that can be taken at any time. We find that the resource constraints and the vaccination and infection costs have a significant impact on the structure of Nash equilibria (NE). In general, the budget constraints can cause NE to become very inefficient, and finding efficient NE as well as the social optimum are NP-hard problems. We develop algorithms for finding NE and approximating the social optimum. We evaluate our results using simulations on different kinds of networks.