1.WELCOME04:36
2.[PAPER: THE NEAREST NEIGHBOUR INFORMATION ESTIMATOR IS ADAPTIVELY NEAR MINIMAX R...05:20
3.Differential Entropy Estimation 05:48
4.Ideas of Nearest Neighbor06:43
5.Kozachenko-Leonenko Estimator07:27
6.Main Result08:30
7.Matching Lower Bound09:11
8.[PAPER: CONTEXTUAL STOCHASTIC BLOCK MODELS]10:36
9.Two paradigms for clustering10:49
10.What if we have both?11:31
11.A statistical model11:51
12.Each individually12:43
13.Our result combines two phase transitions13:24
14.Thank you!14:01
15.[PAPER: ENTROPY RATE ESTIMATION FOR MARKOV CHAINS WITH LARGE STATE SPACE]14:13
16.From Entropy to Entropy Rate15:26
17.Assumption16:21
18.Estimators17:02
19.Main Results18:05
20.Application: Fundamental Limits of Language Models18:47
21.[PAPER: BLIND DECONVOLUTIONAL PHASE RETRIEVAL VIA CONVEX PROGRAMMING]19:31
22.Motivation: Blind Deconvolution Phase Retrieval19:48
23.Blind Deconvolution Phase Retrieval (BDPR): Lifting20:55
24.Novel Convex Relaxation via BranchHull22:01
25.Cartoon of the BranchHull Geometry23:35
26.Main Result: Exact Recovery23:57
27.Phase Portrait for an ADMM Implementation24:10
28.[PAPER: STOCHASTIC CUBIC REGULARIZATION FOR FAST NONCONVEX OPTIMIZATION]24:51
29.(Stochastic) Optimization in Machine Learning25:18
30.Convex Optimization26:12
31.(Stochastic) Gradient Descent27:31
32.Cubic-Regularized Newton Method [Nesterov and Polyak]29:31
33.Question31:01
34.(Pseudo)-SCR Algorithm31:46
35.(Stochastic) Cubic Regularization [Us]33:58
36.AutoEncoder Experiments on MNIST MNIST Deep Autoencoder Results34:52
37.Paper Presentations:35:35
38.Q & A35:40
39.[PAPER: STOCHASTIC NESTED VARIANCE REDUCED GRADIENT DESCENT FOR NONCONVEX OPTIMI...40:01
40.Setup40:08
41.Algorithms & Convergence Results40:39
42.Stochastic Nested Variance Reduced Gradient Descent(SNVRG)41:39
43.Illustration of Update Rules42:34
44.Gradient Complexity Comparison43:33
45.Gradient Complexity Comparison under P-L Condition44:01
46.Thanks!44:20
47.[PAPER: ON THE LOCAL MINIMA OF THE EMPIRICAL RISK]44:37
48.Overview44:48
49.Local Minima45:48
50.Application46:49
51.Almost Sharp Guarantees49:05
52.[PAPER: HOW MUCH RESRICTED ISOMETRY IS NEEDED IN NONCONVEX MATRIX RECOVERY]50:06
53.Nonconvex matrix recovery50:14
54.Exact recovery guarantee 50:46
55.Conclusion answer52:10
56.Counter examples52:32
57.Main Result 53:03
58.Practical Implications53:38
59.How Much Restricted Isometry is Needed in
Nonconvex Matrix Recovery?54:22
60.[PAPER: SPIDER: NEAR-OPTIMAL NON-CONVEX OPTIMIZATION VIA STOCHASTIC PATH-INTEGRA...55:08
61.Problem55:19
62.Comparison of Existing Methods55:50
63.Summary and Extension57:31
64.[PAPER: ANALYSIS OF KRYLOV SUBSPACE SOLUTIONS FOR REGULARIZED NON-CONVEX QUADRAT...58:32
65.Motivation 59:48
66.Challenges in solving large-scale subproblems1:01:07
67.Krylov to the rescue1:01:49
68.Krylov subspace solutions are everywhere 1:03:27
69.Solving the trust-region and cubic problems: Related work1:04:03
70.Our results1:05:00
71.Experiments1:09:09
72.Takeaway1:09:44
73.Q & A1:10:08
74.[PAPER: ESCAPING SADDLE POINTS IN CONSTRAINED OPTIMIZATION]1:14:50
75.Convex Optimization1:15:27
76.Unconstrained optimization1:16:32
77.Constrained optimization: Second-order stationary point1:18:18
78.Main Result1:19:45
79.Poster Information1:20:23
80.[PAPER: CORESETS FOR LOGISTIC REGRESSION]1:20:50
81.Logistic Regression1:21:08
82.How Can We Summarize This Data Set?1:21:40
83.Impossibility Result1:22:30
84.Beyond Worst Case?1:23:31
85.Coreset Construction via Recursive Sampling1:24:13
86.It Even Works In Practice!1:25:02
87.Conclusion and Open Problems1:25:16
88.[PAPER: LEGENDRE DECOMPOSITION FOR TENSORS]1:26:16
89.Our Approach1:26:35
90.Legendre Decomposition1:27:50
91.Information Geometry1:28:42
92.Experimental Results on MNIST1:29:44
93.Summary1:30:08