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Mathematics of Machine Learning: An introduction (Lecture - 01) by Sanjeev Arora
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DISTINGUISHED LECTURES
THREE LECTURES ON MACHINE LEARNING
SPEAKER: Sanjeev Arora (Princeton University and Institute for Advanced Study, USA)
DATE: 12 February 2019 to 13 February 2019
VENUE: Ramanujan Lecture Hall, ICTS Bangalore
Lecture 1: Mathematics of Machine Learning: An introduction
Date & Time: Tuesday, 12 February, 11:30
Abstract: Machine learning is the sub-field of computer science concerned with creating programs and machines that can improve from experience and interaction. It relies upon mathematical optimization, statistics, and algorithm design. The talk will be an introduction to machine learning for a mathematical audience. We describe the mathematical formulations of basic types of learning such as supervised, unsupervised, interactive, etc., and the philosophical and scientific issues raised by them.
Lecture 2: Toward theoretical understanding of deep learning
Date & Time: Tuesday, 12 February, 15:00
Abstract:The empirical success of deep learning drives much of the excitement about machine learning today. This success vastly outstrips our mathematical understanding. This lecture surveys progress in recent years toward developing a theory of deep learning. Works have started addressing issues such as speed of optimization, sample requirements for training, effect of architecture choices, and properties of deep generative models.
Lecture 3: Theoretical analysis of unsupervised learning
Date & Time: Wednesday, 13 February, 11:30
Abstract:Unsupervised learning refers to learning without human-labeled datapoints. This can mean many things but in this talk will primarily refer to learning representations (also called embeddings) of complicated data types such as images or text. Empirically it is possible to learn such representations which have interesting properties and also lead to better performance when combined with labeled data. This talk will survey some attempts to theoretically understand such embeddings and representations, as well as their properties. Many examples are drawn from natural language processing.
0:00:00 ICTS-TIFR: An Overview
0:00:59 ICTS and its Mandate
0:02:50 The ICTS Campus - Imagined (2012)
0:03:06 The ICTS Campus - Realised (2017)
0:04:17 ICTS Research - Structure
0:05:23 ICTS Programs
0:05:28 What ICTS is Not
0:06:06 ICTS Programs - Format
0:07:03 ICTS Programs - Duration
0:08:12 ICTS Programs - Organisation
0:09:10 ICTS Programs - Directions
0:11:24 ICTS Programs - Numbers
0:12:41 ICTS Programs - A Sampling
0:12:56 ICTS Outreach - Initiatives
0:13:28 ICTS Outreach-Kaapi with Kuriosity
0:14:58 Thank You See You Again at ICTS
0:17:00 What is machine learning and deep learning?
0:17:28 Machine learning (ML): A new kind of science
0:19:52 Talk overview
0:20:45 Part 1 - Mathematical formalization of Machine Learning (ML)
0:21:17 Old Idea: Curve fitting (Legendre, Gauss, c. 1800)
0:23:18 Example: Learning to score reviews
0:25:05 Example: Learning to rate reviews (contd)
0:29:01 ML ~ finding suitable function ("model") given examples of desired input/output behavior
0:31:13 Formal framework
0:34:11 Training via Gradient Descent ("natural algorithm")
0:40:35 Subcase: deep learning* (deep models = "multilayered")
0:43:57 Summary so far:
0:56:04 Unsupervised learning (no human-supplied labels)
0:57:39 A Language model (baby "word2ver" [Mikolov et al'1 3])
1:02:47 Properties of semantic word vectors
1:06:54 Sequential decision-making (framework)
1:09:52 Game-playing via Deep Learning (crude account of Alpha-Go Zero)
1:12:45 Part 3 - Toward mathematical understanding of Deep Learning
1:12:52 Special case: deep learning (deep = "multilayered")
1:13:01 Some key questions
1:14:26 Analysis of optimization
1:15:27 Black box analysis (sketch)
1:15:36 More about optimization in next talk, including recent works using trajectory analysis for gradient descent
1:16:10 Why no overfitting?
1:17:11 Part 4 - Taking stock, wrapping up
1:17:40 1. Imitation approach has not worked well in the past: airplanes, chess/go etc.
1:19:02 Sample Task: "Decoding" Brain fMRI [Vodrahalli et al, Neurolmage'17]
1:22:59 Brain regions useful for decoding
1:24:00 Can Machine Learning thrive in India?
1:24:59 Concluding thoughts on ML
1:25:31 Q&A
THREE LECTURES ON MACHINE LEARNING
SPEAKER: Sanjeev Arora (Princeton University and Institute for Advanced Study, USA)
DATE: 12 February 2019 to 13 February 2019
VENUE: Ramanujan Lecture Hall, ICTS Bangalore
Lecture 1: Mathematics of Machine Learning: An introduction
Date & Time: Tuesday, 12 February, 11:30
Abstract: Machine learning is the sub-field of computer science concerned with creating programs and machines that can improve from experience and interaction. It relies upon mathematical optimization, statistics, and algorithm design. The talk will be an introduction to machine learning for a mathematical audience. We describe the mathematical formulations of basic types of learning such as supervised, unsupervised, interactive, etc., and the philosophical and scientific issues raised by them.
Lecture 2: Toward theoretical understanding of deep learning
Date & Time: Tuesday, 12 February, 15:00
Abstract:The empirical success of deep learning drives much of the excitement about machine learning today. This success vastly outstrips our mathematical understanding. This lecture surveys progress in recent years toward developing a theory of deep learning. Works have started addressing issues such as speed of optimization, sample requirements for training, effect of architecture choices, and properties of deep generative models.
Lecture 3: Theoretical analysis of unsupervised learning
Date & Time: Wednesday, 13 February, 11:30
Abstract:Unsupervised learning refers to learning without human-labeled datapoints. This can mean many things but in this talk will primarily refer to learning representations (also called embeddings) of complicated data types such as images or text. Empirically it is possible to learn such representations which have interesting properties and also lead to better performance when combined with labeled data. This talk will survey some attempts to theoretically understand such embeddings and representations, as well as their properties. Many examples are drawn from natural language processing.
0:00:00 ICTS-TIFR: An Overview
0:00:59 ICTS and its Mandate
0:02:50 The ICTS Campus - Imagined (2012)
0:03:06 The ICTS Campus - Realised (2017)
0:04:17 ICTS Research - Structure
0:05:23 ICTS Programs
0:05:28 What ICTS is Not
0:06:06 ICTS Programs - Format
0:07:03 ICTS Programs - Duration
0:08:12 ICTS Programs - Organisation
0:09:10 ICTS Programs - Directions
0:11:24 ICTS Programs - Numbers
0:12:41 ICTS Programs - A Sampling
0:12:56 ICTS Outreach - Initiatives
0:13:28 ICTS Outreach-Kaapi with Kuriosity
0:14:58 Thank You See You Again at ICTS
0:17:00 What is machine learning and deep learning?
0:17:28 Machine learning (ML): A new kind of science
0:19:52 Talk overview
0:20:45 Part 1 - Mathematical formalization of Machine Learning (ML)
0:21:17 Old Idea: Curve fitting (Legendre, Gauss, c. 1800)
0:23:18 Example: Learning to score reviews
0:25:05 Example: Learning to rate reviews (contd)
0:29:01 ML ~ finding suitable function ("model") given examples of desired input/output behavior
0:31:13 Formal framework
0:34:11 Training via Gradient Descent ("natural algorithm")
0:40:35 Subcase: deep learning* (deep models = "multilayered")
0:43:57 Summary so far:
0:56:04 Unsupervised learning (no human-supplied labels)
0:57:39 A Language model (baby "word2ver" [Mikolov et al'1 3])
1:02:47 Properties of semantic word vectors
1:06:54 Sequential decision-making (framework)
1:09:52 Game-playing via Deep Learning (crude account of Alpha-Go Zero)
1:12:45 Part 3 - Toward mathematical understanding of Deep Learning
1:12:52 Special case: deep learning (deep = "multilayered")
1:13:01 Some key questions
1:14:26 Analysis of optimization
1:15:27 Black box analysis (sketch)
1:15:36 More about optimization in next talk, including recent works using trajectory analysis for gradient descent
1:16:10 Why no overfitting?
1:17:11 Part 4 - Taking stock, wrapping up
1:17:40 1. Imitation approach has not worked well in the past: airplanes, chess/go etc.
1:19:02 Sample Task: "Decoding" Brain fMRI [Vodrahalli et al, Neurolmage'17]
1:22:59 Brain regions useful for decoding
1:24:00 Can Machine Learning thrive in India?
1:24:59 Concluding thoughts on ML
1:25:31 Q&A
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