On a 5K screen in Kirkland, Washington, four terminals blur with activity as artificial intelligence generates thousands of lines of code. Steve Yegge, a veteran software engineer who previously worked at Google and AWS, sits back to watch. "This one is running some tests, that one is coming up with a plan. I am now coding on four different projects at once, although really I'm just burning tokens," Yegge says, referring to the cost of generating chunks of text with a large language model (LLM). Learning to code has long been seen as the ticket to a lucrative, secure career in tech.

Self-assessment of one's choices, i.e., confidence, is the topic of many decision neuroscience studies. Computational models of confidence, however, are limited to specific scenarios such as between choices with the same value. Here we present a normative framework for modeling decision confidence that is generalizable to various tasks and experimental setups.

Many manifold learning algorithms aim to create embeddings with low or no distortion (isometric). If the data has intrinsic dimension d, it is often impossible to obtain an isometric embedding in d dimensions, but possible in s > d dimensions. Yet, most geometry preserving algorithms cannot do the latter. This paper proposes an embedding algorithm to overcome this. The algorithm accepts as input, besides the dimensiond, an embedding dimensions d. For any data embedding Y, we compute a Loss(Y), based on the push-forward Riemannian metric associated with Y, which measures deviation of Y from from isometry. Riemannian Relaxation iteratively updates Y in order to decrease Loss(Y). The experiments confirm the superiority of our algorithm in obtaining low distortion embeddings.

In multiplayer games, self-interested behavior among the players can harm the social welfare. Tax mechanisms are a common method to alleviate this issue and induce socially optimal behavior. In this work, we take the initial step of learning the optimal tax that can maximize social welfare with limited feedback in congestion games. We propose a new type of feedback named equilibrium feedback, where the tax designer can only observe the Nash equilibrium after deploying a tax plan. Existing algorithms are not applicable due to the exponentially large tax function space, nonexistence of the gradient, and nonconvexity of the objective. To tackle these challenges, we design a computationally efficient algorithm that leverages several novel components: (1) a piece-wise linear tax to approximate the optimal tax; (2) extra linear terms to guarantee a strongly convex potential function; (3) an efficient subroutine to find the exploratory tax that can provide critical information about the game.

We propose and study a new class of submodular functions called deep submodular functions (DSFs). We define DSFs and situate them within the broader context of classes of submodular functions in relationship both to various matroid ranks and sums of concave composed with modular functions (SCMs). Notably, we find that DSFs constitute a strictly broader class than SCMs, thus motivating their use, but that they do not comprise all submodular functions. Interestingly, some DSFs can be seen as special cases of certain deep neural networks (DNNs), hence the name. Finally, we provide a method to learn DSFs in a max-margin framework, and offer preliminary results applying this both to synthetic and real-world data instances.

The Stochastic Block Model (SBM) is a widely used random graph model for networks with communities. Despite the recent burst of interest in community detection under the SBM from statistical and computational points of view, there are still gaps in understanding the fundamental limits of recovery. In this paper, we consider the SBM in its full generality, where there is no restriction on the number and sizes of communities or how they grow with the number of nodes, as well as on the connectivity probabilities inside or across communities. For such stochastic block models, we provide guarantees for exact recovery via a semidefinite program as well as upper and lower bounds on SBM parameters for exact recoverability. Our results exploit the tradeoffs among the various parameters of heterogenous SBM and provide recovery guarantees for many new interesting SBM configurations.

Online optimization covers problems such as online resource allocation, online bipartite matching, adwords (a central problem in e-commerce and advertising), and adwords with separable concave returns. We analyze the worst case competitive ratio of two primal-dual algorithms for a class of online convex (conic) optimization problems that contains the previous examples as special cases defined on the positive orthant.

We consider the problem of recovering a signal observed in Gaussian noise. If the set of signals is convex and compact, and can be specified beforehand, one can use classical linear estimators that achieve a risk within a constant factor of the minimax risk. However, when the set is unspecified, designing an estimator that is blind to the hidden structure of the signal remains a challenging problem. We propose a new family of estimators to recover signals observed in Gaussian noise. Instead of specifying the set where the signal lives, we assume the existence of a well-performing linear estimator. Proposed estimators enjoy exact oracle inequalities and can be efficiently computed through convex optimization.

Clustering graphs under the Stochastic Block Model (SBM) and extensions are well studied. Guarantees of correctness exist under the assumption that the data is sampled from a model. In this paper, we propose a framework, in which we obtain "correctness" guarantees without assuming the data comes from a model. The guarantees we obtain depend instead on the statistics of the data that can be checked. We also show that this framework ties in with the existing model-based framework, and that we can exploit results in model-based recovery, as well as strengthen the results existing in that area of research.