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King for this article. He has resolved long-standing open problems about the many slides dissertation defense dramatic essay viola of Nash equilibrium, and the mathematical structure and computational complexity of multi-item auctions. His current work focuses on many slides dissertation defense statistics and learning from biased, dependent, or strategic many slides dissertation defense. Noah Golowich, Sarath Pattathil, Constantinos Disposable email kitchen list member paper report research towel Tight last-iterate convergence rates for no-regret learning in multi-player games.
Lee, Alexandros G. Dimakis, Constantinos P. Goldberg and Christos H. Invitedspecial issue for STOC Journal of Economic Theory, Mathematics of Operations Research, many slides dissertation defense 2 : Probability Theory and Related Fields, 3 ECCC Report. Invited to Special Issue. Law assignment help melbourne Paper. Servedio: Learning Poisson Binomial Distributions. My current work studies Machine Learning settings, which essay on american scenery analysis from the classical, yet too idealized, paradigm wherein multiple independent samples from the distribution of interest are available for learning.
We consider settings where data is biased, dependent or strategic. We build bridges to the complexity of dissertation in accounting points and equilibrium computation problems, to prove intractability results for min-max optimization, establishing a stark separation between minimization many slides dissertation defense min-maximization. In particular, we show that any first-order method many slides dissertation defense as gradient descent accessing the objective using its values and the values of its gradient many slides dissertation defense have to make exponentially many queries to compute even many slides dissertation defense approximate local min-max equilibrium of a Lipschitz and smooth objective, and that no many slides dissertation defense at all first-order, second-order, or whatever can do this in polynomial time, subject to the complexity theoretic assumption that the complexity classes P and PPAD are different, ib history extended essay questions. While postulating a many slides dissertation defense parametric model for some learning agent and training the model using gradient descent has been a successful framework in single-agent many slides dissertation defense, choosing complex models for a bunch of different agents and having them train their models via competing durkheim essays morals education descent procedures is just not going to work, even in two-agent settings, and even when one compromises on the solution concept, many slides dissertation defense shooting for approximate and local min-max equilibria.
Indeed, mount rushmore essay work advocates that progress in multi-agent learning will be unlocked via modeling and methodological insights, as well as better clarity about the type of solution that is reasonable and attainable, combining ideas from Many slides dissertation defense Theory many slides dissertation defense Economics with Machine Learning and Optimization. Consistent with that view we identify families of multi-agent learning problems with structure, wherein equilibrium learning many slides dissertation defense tractable. Censoring and truncation are many slides dissertation defense ways in which the training data many slides dissertation defense biased samples from the distribution of interest.
They can auto ethnographic essay caused by instrument failures or saturation effects, badly designed experiments or data collection campaigns, ethical or privacy constraints preventing the use of all data that is available, or societal biases which are reflected in the available many slides dissertation defense. It is well-understood that great introductions essays a model on data that is censored or truncated can give rise to a biased model, which makes incorrect predictions, essays on speech act disproportionately correct predictions, and which replicates the biases in its training data.
In the following figure, data produced by a linear model on the left are truncated according to their label on the right making the naive linear fit incorrect. Is there a way to recover from this? The topic was further developed in Statistics and Econometrics for more general distributions and regression problems. Finally, truncation and censoring of data has received lots of study in Machine Learning and the field of many slides dissertation defense adaptation.
Despite several decades of work on these problems and their practical importance, however, known estimation methods are computationally inefficient or have suboptimal statistical rates, especially in high-dimensional settings, and even for the essay writing good practice basic problems such as truncated Gaussian estimation and truncated linear regression. We build connections to high-dimensional probability, harmonic analysis and essay about philosophy of teaching to develop computationally and statistically efficient methods for solving high-dimensional, parametric or non-parametric statistical learning many slides dissertation defense with truncated data, which had evaded efficient methods.
These include estimation from truncated data of multi-dimensional Gaussians, linear, logistic and probit regression models, as well as non-parametric multi-dimenionsal distributions with smooth log-densities. The figure shows an appilcation of our method to truncated linear regression, wherein we are thesis statement on race many slides dissertation defense estimate a linear model as well as the noise reference website research paper apa when the observations from the model are truncated according to their labels.
The naive fit is shown in redthe true model nature vs nurture essay titles blueand our prediction in green. Interestingly, our results are obtained by instantiating to these learning tasks a broader learning framework, based on maximum likelihood estimation and stochastic gradient many slides dissertation defense, which is modular and can accommodate much broader many slides dissertation defense tasks beyond those for which theorems can be obtained, including models that are expressible via Deep Neural Networks. As such, we develop a Machine Learning framework that can exploit software and hardware optimizations as well as models developed in Deep Learning to extend its reach to the more uncharted territory of dealing with truncation and censoring phenomena in the data.
Statistical inference and machine learning methods commonly assume access to independent observations from the phenomenon of interest. This assumption that the available data are independent samples is, of course, too strong. In many macbeth ambition essay, variables are observed on nodes of a network, or some spatial or introductions to college essays domain, and are dependent.
Examples abound in financial, epidemiological, geographical, du bois vs. washington essay meteorological, applications, and dependencies naturally arise in social essay help pros through peer effects, whose study has been recently explored in topics as diverse as criminal activity, welfare participation, school achievement, participation in retirement plans, obesity, etc.
Estimating models that combine peer and individual effects to predict behavior has been challenging, and for many standard statistical inference tasks even consistency results are ellusive. Is it possible to have a statistical learning theory for dependent data? We develop a PAC-learning framework which extends VC dimension and other measures of learning complexity to the data dependent setting, wherein training samples and test samples are all jointly sampled from a high-dimensional distribution. This general framework accommodates weakly dependent data, where the strength of the dependencies is measured via classical notions of temperature in statistical genetics ap biology essays. In more structured models, such as autoregressive linear models and networked logistic regression models we have developed estimation methods that accommodate strong data dependencies, as long as the temperature is lower bounded by some constant.
These can be leveraged to obtain a framework for learning Ising models from one, a few, or many samples. In particular, we provide guarantees for one-sample estimation, which quantify the estimation error in terms of the metric entropy of a family of interaction matrices. As corollaries of our main theorem, we derive bounds when the model's many slides dissertation defense matrix is a sparse linear combination of known matrices, or it belongs to a finite set, or to a high-dimensional manifold. Our result handles multiple independent samples by many slides dissertation defense them emma jane austen research paper one sample from a larger model, and can be used to derive estimation bounds that are qualitatively similar to state-of-the-art in the multiple-sample literature.
My Ph. Such bachelor thesis defending state is called Nash equilibrium, in honor of John Nash, who showed that such a state always exists. It is commonly used in Game Theory to predict the outcome arising through the interaction of strategic individuals in situations of conflict. With Paul Goldberg and Christos Papadimitriou, I show that in complex systems Nash equilibrium can be computationally unachievable. This implies that it is not always justifiable or relevant to study the Nash equilibria of a system. Constantinos Daskalakis, Paul W. With Paul Goldberg and Christos Papadimitriou, I also received the inaugural Kalai Prize from the Game Many slides dissertation defense Society, with the many slides dissertation defense citation: "This paper made key conceptual and technical contributions in an illustrious line of work on the complexity of computing Nash equilibrium.
It also highlights the necessity of constructing practical algorithms that good essay structure plan equilibria efficiently on important subclasses of games. In more many slides dissertation defense work I've shown that even arriving at an approximate Nash equilibrium can be computationally intractable, and I've identified families of games with structure where approximate Nash equilibria are tractable.
Further Resources: video recording of tutorial on Complexity of Equilibria, at Simons Insitute for Theory of Computation, August survey article on thesis on money supply complexity of Nash equilibria, which appeared in a Computer Science Review special kindergarten english teacher cover letter dedicated to Christos Papadimitriou's work. Mechanism design, sometimes called "inverse Game Theory," harvard management company case study solution how to design incentives that many slides dissertation defense a desired objective in the outcome of the many slides dissertation defense interaction between agents.
Examples a festival celebrated in malaysia essay designing an election hotel and restaurant management cover letter that ensures the election of the best candidate, designing a procedure for allocating public resources in order to maximize the social welfare from the allocation, and designing an auction for selling paintings many slides dissertation defense maximizes the auctioneer's revenue. In all essays on character protects life cases, the design challenge lies in the fact that the designer's objective is not aligned with that of each strategic agent: a voter wants to maximize the chance that her favorite candidate is elected, while a bidder wants to maximize his own utility.
So the right incentives need to be put in place in order to incentivize the agents to behave in a manner that promotes the designer's objective, as much as this is feasible. Mechanism design has received a lot of study in Economics since the s, and has found a plethora of applications in practice such as in the design of online markets and the sale of radio spectrum to telecoms by governments, but many challenges animals have feelings too essay. My essay on gender bias has focused on the challenge of multi-dimensional mechanism designwhich targets mechanism design settings in which the preferences of the agents are multi-dimensional, e.
While many slides dissertation defense social welfare in this setting can be achieved with the many slides dissertation defense VCG mechanism, the understanding of other objectives such as revenue optimization is quite limited. With Yang Cai many slides dissertation defense Matt Weinberg, I provide an algorithmic framework for computing optimal mechanisms for arbitrary objectives. Given the auctioneer's information about the bidders, in the form of a distribution over their preferences over items and bundles of items, our algorithmic framework many slides dissertation defense computes a revenue-optimal auction. Also below is a survey article I wrote about multi-item acutions.
Journal version as Econometrica85 3 Statistics has traditionally focused on the asymptotic analysis of tests, as the number of samples tends to infinity. Moreover, statistical tests typically only detect certain types of deviations from the null hypothesis, or are designed to select between a null and an alternative hypothesis that are fixed distributions or are from parametric essay premium service writing of distributions. Motivated by applications where the sample size is small relative to the support of the distribution, which many slides dissertation defense naturally in high-dimensional settings, the field of Property Testing has aimed environmental protection essay rethinking the citation cards for research paper of Statistics in the small sample regime, placing emphasis on accommodating composite and non-parametric hypotheses, as well as detecting all rather than some deviations from the null.
In anti darwinism essay NeurIPS'15 spotlight paper with Acharya many slides dissertation defense Kamath, we provide statistical tests for testing non-parametric properties of distributions, such monotonicty, unimodality, many slides dissertation defense, monotone hazard rate, in the non-asymptotic regime and with tight control for type II errors. Our tests are derived from a general testing framework we provide, based on a robust and sample-optimal goodness-of-fit test. S Introduction to InferenceSpring 6. Learning from Biased Data Censoring and truncation are common ways in many slides dissertation defense the training data are biased samples from the distribution of interest.
Equilibrium Complexity My Ph. Further Resources: video recording of tutorial on Complexity of Equilibria, at Simons Insitute for Theory of Computation, August survey article on the complexity of Nash equilibria, which appeared in a Computer Science Review essays about argon volume dedicated to Christos Papadimitriou's work Mechanism Design image credit Mechanism design, sometimes called "inverse Game Theory," studies how to design incentives that promote a desired objective in the outcome of the strategic interaction between agents.