STAT 513/413: Lecture 22 EM Algorithm (A big splash in the maximum likelihood world) Not everything has to be done numerically We may sometimes solve the problem in closed form And sometimes, we may solve by numerics only some part of it EM Algorithm: a general scheme for reducing (some) more difficult problems into a […]
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Computable Functions Co-hosted by: Yousef Akiba Turing Computability • We learnt about Turing Machines • A function is Turing computable if there is a TM that can compute it • The Turing thesis (Faith): Every intuitively computable function is Turing computable Gödel’s approach • Recall that Gödel started with initial functions • Zero function (z),
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STAT 513/413: Lecture 23 Iteratively Reweighted Least Squares (A dubious relative) Recall: Cauchy regression yi = xTi β + σεi with εi Cauchy errors (and σ known) The EM-algorithm: select β1 Calculate weights zi = 1 1 + ( y i − x Ti β 1 ) 2 σ2 Calculate β2 as a weighted least
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STAT 513/413: Lecture 20 Walking hills and ravines (A refresment of calculus) Hills and ravines One-dimensional case too trivial to bother with Multi-dimensional cases too difficult to imagine/picture The only one that somewhat can be: the two-dimensional case hills = maximization ravines = minimization Some map reading experience may be handy – in particular, when
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COMP3221: Distributed Systems Time Synchronization Unit Coordinator Dr Nguyen Tran School of Computer Science The University of Sydney Page 1 Time matters…ex. (1) – A bank replicates two copies of an account database in New York City (NYC) and San Francisco (SF) so that a query is always forwarded to the nearest city while updates
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COSC 2673/2793 | Machine Learning Week 5 Lab Exercises: **Training a Classification Model & Typical ML process** Introduction During the last couple of weeks we learned about how to read data, do exploratory data analysis (EDA) and prepare data for training and training a ML model. However, we did not specifically discuss the typical ML
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COMP3221: Distributed Systems Introduction Dr Nguyen Tran School of Computer Science The University of Sydney Page 1 Outline – Why this course ? – What this course is about? – Definitions, Examples and Challenges of Distributed Systems – Course Logistics – Lectures/Tutorials – Assessments – Expectation and Outcomes – Resources The University of Sydney Page
NP No Problem! Definition 1 • 𝑁𝑃 = {𝐿: 𝐿 decidable by a polynomial time nondeterministic TM} )𝑘𝑛(𝐸𝑀𝐼𝑇𝑁N∈𝑘ڂ =𝑃𝑁• = 𝑛𝑓𝐸𝑀𝐼𝑇𝑁• {𝐿: 𝐿 is a language decidable by an 𝑂 𝑓 𝑛 nondeterministic TM} 𝑃𝑁 ⊆ 𝑃 •  Running Time for nondeterministic TMs • is the maximum number of steps the TM uses on
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CSE240 Chapter 5 Logic Language Prolog Lecture 27 More recursive programs, Pairs and Lists Reading: Textbook Sections 5.4 and 5.5 Dr. Yinong Chen CSE240 Introduction to Programming Languages ‹#› Ch 5 CSE240 11/19/2002 Introduction Logic programming paradigm Prolog programs: facts, rules, and goals Factbase Goals (Questions) Rulebase Compound questions Arithmetic operations and rules Recursion and
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PATH • Given a directed graph G and two nodes 𝑠, 𝑡 in 𝐺. Question: Isthereapathfromstot? • 𝑃𝐴𝑇𝐻 = { 𝐺,𝑠,𝑡 :𝐺isadirectedgraphthathasadirectedpathfrom𝑠to𝑡} Is 𝐺,𝑠,𝑡 ∈𝑃𝐴𝑇𝐻? • This is a stronger question than the first one. It hides more questions: Is 𝐺 𝑎 directed graph? Are 𝑠, 𝑡 vertices in 𝐺? Theorem: PATH ∈ 𝑃 •
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