Search

19 Nov 2023: Z =aA. bB. cC. dD. eE. g1(A = a, C = c)g2(B = b, C = c, D = d)g3(C = c, D = d, E = e). ... A. D. C. B. E. A. D. C. B. E(a) (b) (c).

19 Nov 2023: b. ],[A B. B> C. ])= p(x|y) = N(a BC1(y b), ABC1B>),. ... For Gaussians:. p(fi, f<i) = N([ a. b. ],[A B. B> C. ])=

19 Nov 2023: b. ],[A B. B> C. ])= p(x|y) = N(a BC1(y b), ABC1B>),. ... For Gaussians:. p(fn, f<n) = N([ a. b. ],[A B. B> C. ])=.

19 Nov 2023: p(x, y) = p([ x. y. ])= N. ([ ab. ],[. A B. B> C. ]),. we get the marginal distribution of x, p(x) by. ... For Gaussians:. p(fn, f<n) = N([ a. b. ],[A B. B> C. ])=.

19 Nov 2023: How many documents, how many words and how many unique words are there inA, in B and in the union of A and B? ... What is the per-wordperplexity? What is the per-word perplexity over all documents in B?

19 Nov 2023: How manydocuments, how many words and how many unique words are there in A, in B and in the union of Aand B? ... What is theper-word perplexity over all documents in B? f) 10% : What would the perplexity be for a uniform multinomial?

19 Nov 2023: p(x, y) = N([ a. b. ],[A B. B> C. ])= p(x|y) = N(aBC1(yb), ABC1B>),. ... b. ],[A B. B> C. ])= p(x|y) = N(aBC1(yb), ABC1B>). Do try this at home!

19 Nov 2023: Some distributions (cont). Uniform (x [a,b]):p(x|a,b) =. {1ba if a x b0 otherwise. ... Gamma (x 0):p(x|a,b) = b. a. Γ(a)xa1 exp{bx}. Beta (x [0, 1]):p(x|α,β) = Γ(α β).

19 Nov 2023: p(x, y) = N([ a. b. ],[A B. B> C. ])= p(x|y) = N(aBC1(yb), ABC1B>),. ... b. ],[A B. B> C. ])= p(x|y) = N(aBC1(yb), ABC1B>). Do try this at home!

19 Jun 2024: Z. (b). X. Y. Z. 12 / 26. D-separation (“directed separation”) in Bayesian networks. ... over A,B,C :. p(D) =a,b,c. p(A = a,B = b,C = c,D). 28 / 26.

19 Jun 2024: over A,B,C :. p(D) =. a,b,c. p(A = a,B = b,C = c,D). 8 / 32. ... c. b. a. p(D | c)p(c | b)p(b | a)p(a).

19 Jun 2024: ergy. ES. B. (a) W = 1. 0 0.5 10.8. 0.6. ... B. (b) W = 1.38. 0 0.5 10.4. 0.3. 0.2. 0.1.

19 Jun 2024: More precisely,let b′ = ⟨b, ,b⟩ Rnk0 be a k-replication of b. ... That is, forany b R0, I(b,b, ,b) = 0. In addition to the above four principles satisfied by many in-equality indices, we also focus on the following property whichis

19 Jun 2024: Let B be a set satisfying diam(B) B for someuniversal constant B that does not depend on d (B mightbe for instance a unit sphere). ... Gretton, A., Borgwardt, K. M., Rasch, M. J., Schölkopf, B.,and Smola, A.

19 Jun 2024: Let P ={x Rm|Ax b} be a polytope for some A =[a1,. ... ak]. > Rkm, b Rk (for some k N). Thenfor v Ext(P), we have.