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"Probabilistic Programming for Machine Learning"
امیرعباس اسدی
Bayesian Learning provides a natural framework for approaching Machine Learning problems. For a long time, due to the significant computational cost of Bayesian inference, this framework was limited to simple models and problems with a small amount of data. Probabilistic Programming is the fruit of many years of research in approximate Bayesian inference aiming to address these limitations. This presentation is a friendly introduction to Probabilistic Programming. We will explore how modern inference methods and recent advances in Differentiable Programming can help us unlock the full potential of Bayesian Machine Learning.
Presentation outline:
- Bayesian Learning and Probabilistic Programs
- Probabilistic Programming in Julia
- Approximate Bayesian Inference
-- Markov Chain Monte Carlo
-- Variational Inference
- Differentiable Programming
- Discussing some examples:
-- Bayesian Deep Learning
-- Bayesian Neural Differential Equations
-- Inverse Optimization
پیشنیاز های علمی: آمار و احتمال مقدماتی، آشنایی با Deep Learning
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سلسله جلسات گذر
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How to Count with Polynomials?
میلاد برزگر، محقق پسادکتری پژوهشگاه دانشهای بنیادی (IPM)
Counting perfect matchings in bipartite graphs is a fundamental problem in theoretical computer science (TCS) and combinatorial optimization. In TCS, the goal is to find (approximation) algorithms, and in combinatorics, the aim is to bound the number of perfect matchings in a specific class of graphs. In this talk, I will focus on regular bipartite graphs and discuss (1) deterministic approximation algorithms for the number of perfect matchings in these graphs, and (2) the Schrijver-Valiant conjecture, which determines the minimum number of perfect matchings in d-regular bipartite graphs of a given size. This conjecture was proposed by Schrijver and Valiant in 1980 and resolved by Schrijver in 1998. Schrijver’s proof is considered to be one of the most complicated and least understood arguments in graph theory!
One of the high points of matching counting (!) is Leonid Gurvits’ ingenious work in the early 2000s. He came up with a neat elementary argument for both (1) and (2). In fact, he created a machinery known as the “capacity method” that has since found many more applications. Gurvits’ approach is based on the “geometry of polynomials,” which is the study of the analytic properties of (multivariate) polynomials with complex or real coefficients. This work kick started a new trend known as the “polynomial paradigm.” Over the last two decades, people have used tools from the geometry of polynomials to solve a number of notorious open problems in mathematics and TCS. In this talk, I will go through Gurvits’ argument and the consequences of his ideas. In particular, I will try to highlight the importance of the notion of “capacity” and its applications in counting and optimization.
پیشنیاز های علمی: آشنایی با جبرخطی و احتمال
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چندجملهایهای لورنتزی و تقریب زدن دنبالههای لگاریتم محدب
مریم محمدی یکتا، کارشناسی ارشد دانشگاه واترلو
در این ارائه، چندجملهایهای لورنتزی و لورنتزی دینرمالایزد شده (denormalized Lorentzian) را معرفی میکنیم. این چندجملهایها ارتباط نزدیکی با دنبالههای لگاریتم محدب دارند و میتوان با کمک آنها، کران بالایی برای برخی از این دنبالهها یافت. به طور مثال، میتوان تعداد ماتریسهای m×n که جمع هر سطر و هر ستون آن داده شده باشد، یا تعداد جریانهای یک گراف جهتدار که جریان گذرا از هر رأس آن داده شدهباشد را با کمک این چندجملهایها تقریب زد که در این ارائه به آنها خواهیم پرداخت.
پیشنیاز های علمی: ریاضی ۲- آشنایی با گرافها
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Non-Interactive Key-Exchange Protocols
الهه صادقی
In this work, we initiate a study of
K-NIKE protocols in the fine-grained setting, in which there is a polynomial gap between the running time of the honest parties and that of the adversary. Our goal is to show the possibility, or impossibility, of basing such protocols on weaker assumptions than those of
K-NIKE for K >= 3.
We improve the security by further using algebraic structures, while avoiding pairings. In particular, we show that there is a 4-party NIKE in Shoup's generic group model with a quadratic gap between the number of queries by the honest parties vs. that of the adversary.
پیشنیاز های علمی:
Basic Knowledge of Group Theory and Cryptography.
I will explain the intuition behind every part of the lecture though, so everyone are welcome to join.
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