# Stanford Theory Seminar

Stanford Theory Seminar (formerly known as Stanford
Algorithms Seminar/AFLB) is usually held in Gates 498 or Theory Lounge(Gates
463A)

Faculty Contact: Mary Wootters

Student Contact: Shashwat Silas

Click here for directions.

## October 26, 2017

Gates 463A, 4:15PM
## Raghu Meka (UCLA)

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Learning discrete Markov Random Fields with nearly optimal runtime and sample complexity.

We give an algorithm for learning the structure of an undirected graphical model that has essentially optimal sample complexity and running time. We make no assumptions on the structure of the graphical model. For Ising models, this subsumes and improves on all prior work. For general t-wise MRFs, these are the first results of their kind.
Our approach is new and uses a multiplicative-weight update algorithm. Our algorithm-- Sparsitron-- is easy to implement (has only one parameter) and holds in the online setting. It also gives the first provably efficient solution to the problem of learning sparse Generalized Linear Models (GLMs).

Joint work with Adam Klivans.

## October 19, 2017

Gates 463A, 4:15PM
## Rasmus Kyng (Simons)

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Approximate Gaussian Elimination for Laplacians

We show how to perform sparse approximate Gaussian elimination for Laplacian matrices. We present a simple, nearly linear time algorithm that approximates a Laplacian matrix by a matrix with a sparse LU factorization. We compute this factorization by subsampling standard Gaussian elimination. This gives the simplest known nearly linear time solver for Laplacian equations. It is a significant step towards practical and provably correct algorithms for this problem. The crux of our proof is the use of matrix martingales to analyze the algorithm.
Joint work with Sushant Sachdeva.

## October 12, 2017

Gates 463A, 4:15PM
## Thatchaphol Saranurak (KTH)

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Dynamic Spanning Forest: Techniques and Connections to Other Fields

I will first give an overview of dynamic algorithms and their connections to other fields. Then, I will present our recent progress on the question "is there a dynamic algorithm with small worst-case update time" for the spanning forest problem, which is among central problems in dynamic algorithms on graphs. Our result guarantees an n^{o(1)} worst-case update time with high probability, where n is the number of nodes. The best worst-case bounds prior to our work are (i) the long-standing O(\sqrt{n}) bound of [Frederickson STOC'83, Eppstein, Galil, Italiano and Nissenzweig FOCS'92] (which is slightly improved by a O(\sqrt{\log(n)}) factor by [Kejlberg-Rasmussen, Kopelowitz, Pettie, Thorup ESA'16]) and (ii) the polylogarithmic bound of [Kapron, King and Mountjoy SODA'13] which works under an oblivious adversary assumption (our result does not make such assumption).
The crucial techniques are about expanders: 1) an algorithm for decomposing a graph into a collection of expanders in near-linear time, and 2) an algorithm for "repairing" the expansion property of an expander after deleting some edges of it. These techniques can be of independent interest.

This talk is based on results by [Nanongkai, Saranurak and Wulff-Nilsen, FOCS'17], [Nanongkai and Saranurak, STOC'17] and [Wulff-Nilsen, STOC'17].

## October 5, 2017

Gates 463A, 4:15PM
## Rad Niazadeh (Stanford)

### Bernoulli Factories and Blackbox Reductions in Mechanism Design

In this talk, I am going to talk about a recent polynomial-time reduction from Bayesian incentive-compatible mechanism design to Bayesian algorithm design for welfare maximization problems. Unlike prior results, our reduction achieves exact incentive compatibility for problems with multi-dimensional and continuous type spaces. The key technical barrier preventing exact incentive compatibility in prior black-box reductions is that repairing violations of incentive constraints requires understanding the distribution of the mechanism’s output, which is typically #P-hard to compute. Reductions that instead estimate the output distribution by sampling inevitably suffer from sampling error, which typically precludes exact incentive compatibility. We overcome this barrier by employing and generalizing the computational model in the literature on Bernoulli Factories.
In a Bernoulli factory problem, one is given a function mapping the bias of an “input coin” to that of an “output coin”, and the challenge is to efficiently simulate the output coin given only sample access to the input coin. I will show how to incorporate Bernoulli factories to design a polynomial time algorithm for the following selection problem: a ground set of elements and sampling oracles for each element are given (for unknown input distributions), expected values of the input distributions correspond to the weights of the elements in the set, and we wish to select an element with probability proportional to an exponential function of its weight by efficient sampling. I then show how this algorithm solves a simple single agent truthful mechanism design problem. This truthful mechanism is the key ingredient that can be used to make the approximately incentive compatible reduction of Hartline et al. (2015) exactly incentive compatible.
This talk is based on a joint-work with Shaddin Dughmi, Jason Hartline, and Bobby Kleinberg.

## September 28, 2017

Gates 463A, 4:15PM
## Shengwu Li (Harvard)

### Credible Mechanism Design

Consider an extensive-form mechanism, run by an auctioneer who communicates sequentially and privately with agents. Suppose the auctioneer can make any deviation that no single agent can detect. We study the mechanisms such that it is incentive-compatible for the auctioneer not to deviate -- the credible mechanisms. Consider the ex post individually-rational optimal auctions. The first-price auction is the unique sealed-bid credible mechanism. The ascending auction is the unique strategy-proof credible mechanism.