Professor Zhang Zhihua: machine learning--a love of statistics and computation

Professor Zhang Zhihua: machine learning--a love of statistics and computation

Editorial press: This article is from Zhang Zhihua teacher in the ninth China R Language Conference and Shanghai Jiaotong University's two lectures in the sorting out. Zhang Zhihua is a professor of computer science and engineering at Shanghai Jiaotong University, adjunct professor of data Science Research Center of Shanghai Jiaotong University, doctoral tutor in computer science and technology and statistical studies. Before joining Shanghai Jiaotong University, he was a professor of computer science and a adjunct professor at Zhejiang University. Mr. Zhang is mainly engaged in teaching and research in the field of artificial intelligence, machine learning and applied statistics, and has published more than 70 papers in major international academic journals and important computer science conferences, and is a guest commentator on "Mathematics review" in the United States, and the International Machine learning flagship publication journal Executive editorial Board of Learning. His open course, Introduction to machine learning and statistical machine learning, has received wide attention.

Zhang Zhihua teacher and his students

Hello everyone, today my speech theme is " Machine learning: Statistics and Computing love ." I used a very romantic name, but I was in a state of trepidation. I am afraid I am not able to control such a big theme, and two I am actually a puzzled amorous feelings, some of my views may not meet the mainstream voice of domestic academia.

The recent strong rise in AI or machine learning, especially in the past Alphago and Korean chess players Li Shishi Nine segments of the man-machine war, once again let us appreciate the great potential of artificial intelligence or machine learning technology, but also deeply touched me. In the face of this unprecedented technological change, as the more than 10 years has been engaged in the study of the first line of statistical machine learning and research scholars, I hope to take this opportunity to share with you some of my personal thinking and reflection.

In this event of artificial intelligence development, I suddenly found that for our Chinese scholars, it seems to be a group of onlookers watching lively. Whether you admit it or not, the truth is that with my generation or earlier scholars can only be a spectator. What we can do is to help you---the young generation of China, to make you competitive in the tide of artificial intelligence, to make benchmarking achievements, to create the value of human civilization, and let me have a cheering home team.

My speech mainly consists of two parts, in the first part, a brief review of machine learning development, which explores the intrinsic nature of machine learning phenomena, especially the relationship between it and statistics, computer science, logistics optimization and other disciplines, as well as its relations with industry, the entrepreneurial community. In the second part, we try to use the concepts of "multilevel", "adaptive" and "average" to simplify the research ideas or ideas behind the numerous and colorful machine learning models and computational methods.

Part I: Review and reflection 1. What is machine learning

There is no doubt that big data and artificial intelligence are the most fashionable nouns today, and they will bring profound changes to our future lives. Data is fuel, intelligence is the goal, and machine learning is the rocket, the technological pathway to intelligence. Machine learning guru Mike Jordan and Tom Mitchell that machine learning is a cross between computer science and statistics, and is at the heart of AI and data science.

"It is one of today's rapidly growing technical fields, lying at the intersection of computer, and statistics, and At the core of artificial intelligence and Data science "-- -M. Jordan

In layman's terms, machine learning is about digging out useful values from data. The data itself is dead, and it does not automatically render useful information. How do you find something that is valuable? The first step is to give the data an abstract representation, then modeling based on the representation, then estimating the parameters of the model, that is, the calculation, in order to deal with the problems caused by large-scale data, we also need to design some efficient means of implementation.

I explain this process as machine learning equals Matrix + statistics + optimization + algorithm . First, when the data is defined as an abstract representation, it often forms a matrix or a graph, which can be understood as a matrix. Statistics is the main tool and way of modeling, and the model solving is mostly defined as an optimization problem, especially, the frequency statistic method is an optimization problem in fact. Of course, the calculation of Bayesian models involves random sampling methods. When it comes to the implementation of big data, there are a number of efficient ways to do it, and the algorithms and data structures in computer science can help us solve this problem.

Drawing on Marr's definition of three-level theory of computer vision, I have also divided machine learning into three levels: beginner, intermediate, and advanced. The primary stage is data acquisition and feature extraction. Intermediate stage is data processing and analysis, it contains three aspects, the first is the application of problem-oriented, in short, it mainly applies the existing models and methods to solve some practical problems, we can be understood as data mining, second, according to the needs of application problems, the proposed and development of models, Methods and algorithms, as well as the mathematical principles or theoretical foundations that underpin them, I understand that this is the core of the machine learning discipline. Third, by reasoning to achieve some kind of intelligence. Finally, the advanced stage is intelligence and cognition, that is, the goal of achieving intelligence. From here, we see that data mining and machine learning are essentially the same, the difference is that data mining is more grounded on the database side, and machine learning is closer to the smart side.

2, the development of machine learning process

Let's comb the course of machine learning. Before the 90 's, I didn't know enough about it, but I felt that machine learning was in a dull phase of development. The 1996-2006 is its golden period, the main symbol is the emergence of a number of important achievements in academia, for example, based on statistical learning theory, such as SVM and boosting classification methods, based on the regenerative kernel theory of non-linear data analysis and processing methods, with Lasso as the representative of the sparse learning model and application, and so on. These results should be the work of both the statistical community and the computer science community.

However, machine learning has also undergone a brief period of wandering. I felt it, because at the end of my post-doctoral work at Berkeley, I was facing a job search, so my mentor Mike Jordan and I had a lot of conversations, and he thought that machine learning was in a difficult period, the job was getting full, and he repeatedly stressed to me The idea of introducing statistics into machine learning is right, since the status of machine learning based on statistics as a discipline has been laid. The main problem is that machine learning is an applied discipline, and it needs to play a role in industry to solve practical problems for them. Fortunately, this period soon passed. Perhaps most of us here are not impressed by this period, because China's academic development tends to be slower than half a shot.

Now we can confidently say that machine learning has become a major subject of computer science and artificial intelligence. Mainly reflected in the following three iconic events.

First, in February 2010, Professor Mike Jordan of Berkeley and Professor Tom Mitchell of CMU were selected as academician of the American Academy of Engineering, and in May, the statisticians of Mike Jordan and Stanford, Jerome Friedman, were elected as Fellow of the United States College of Sciences. We know that many well-known machine learning algorithms such as cart, MARS and GBM are presented by Professor Friedman.

In the following years, a number of scholars who made important contributions to machine learning were selected as academicians of the American Academy of Sciences or engineering. For example, AI expert Daphne Koller, boosting's main creator Robert Schapire, Lasso's author Robert Tibshirani, Chinese famous statistical learning expert journal teacher, statistical machine learning expert Larry Wasserman, the famous optimization algorithm expert Stephen Boyd et. At the same time, machine learning experts, deep learning leaders Toronto University Geoffrey Hinton, and the school's statistical learning expert Nancy Reid, were selected as foreign academicians of the American Academy of Engineering and Sciences respectively this year.

That was when Mike congratulated me on his return to the Academy:

Thanks for your congratulations in my election to the national Academy. It's nice to has machine learning recognized in the this.

Therefore, I understand that whether a subject in the United States can be accepted as a major subject is an important sign of whether or not a scientist can be elected as an academician. We know that Tom Mitchell is the early founder and guardian of Machine learning, and Mike Jordan is the founder and catalyst of statistical machine learning.

This selection mechanism is undoubtedly advanced, it can promote the benign development of disciplines, adapt to social dynamic development and demand. Conversely, if XXX is selected as a national academician in some way, then they have mastered the country's academic discourse and the right to allocate resources. Such a mechanism may cause problems, such as the excessive development of resources in some excess disciplines or sunset disciplines, and the marginalization of mainstream disciplines.

Second, the 2011 Turing Award was awarded to Professor Judea Pearl of UCLA, whose main areas of study are probabilistic mapping models and causal reasoning, which is the fundamental problem of machine learning. We know that the Turing Award is usually awarded to scholars who do pure theoretical computer science, or to the early establishment of computer architecture, and the Turing Award to Professor Judea Pearl has the meaning of direction.

Third, the current hot spots, such as deep learning, AlphaGo, driverless cars, artificial intelligence assistants and so on to the industry's huge impact. Machine learning can actually be used to help industry solve problems. There is a lot of demand for talent lady in the field of machine learning, not just engineers with strong code skills, but also scientists with mathematical modelling and problem solving.

Let's look at the relationship between industry and machine learning in concrete detail. I have been in the Google Research Institute for a year of visiting scientists, I have a lot of colleagues and former students in the IT industry, usually the laboratory also often receives some company visits and exchanges, so understand some it situation.

I understand that today's IT development has shifted from the traditional Microsoft model to the Google model. The traditional Microsoft model can be understood as manufacturing, while the Google model is the service sector. Google search is completely free, service society, their search to do more and more extreme, while creating more and more rich wealth.

Wealth resides in data, and the core technology that digs it is machine learning. Deep learning, as one of the most dynamic machine learning directions in the world, is a disruptive achievement in computer vision, natural language comprehension, speech recognition, and intelligence games. It has created a group of emerging startups.

3. Statistics and calculation

My focus is still to go back to academia. Let's focus on the relationship between statistics and computer science. Larry Wasserman, a professor at the CMU Department of Statistics, has recently been selected as a Fellow of the American Academy. He wrote a book with a very overbearing name, all of Statistics. There is a very interesting description of statistics and machine learning in the introductory part of the book. He thinks the original statistics are in the Department of Statistics, the computer is in the computer system, these two are not connected, and each other does not agree with each other's value. Computer theorists think that statistical theory is useless and does not solve the problem, while statisticians think that computer science is just re-building the wheel, no novelty. However, he believes the situation is now changing, and statisticians recognize the contribution that computer theorists are making, while computer theorists recognize the universal significance of statistical theory and methodology. So, Larry wrote this book, it can be said that this is a statistical scholar wrote the computer field of books for computer scholars to write the book of the field of statistics.

Now there's a consensus: if you're using a machine-learning approach that doesn't understand its fundamentals, it's a horrible thing to do. For this reason, the academic community is still skeptical about deep learning. Deep learning has demonstrated the effectiveness of its powerful practical applications, but the principles are not yet known.

Let's further analyze the relationship between statistics and computers. Computer theorists often have strong computational power and problem-solving intuition, while statisticians have a strong ability to model and analyze, so they have good complementarity.

Boosting, SVM and sparse learning are the machine learning community as well as the statistical community, in the last decade or nearly 20 years, the most active direction, it is now difficult to say who is more than who contributed to the greater. For example, the theory of SVM is actually very early vapnik and so on, but the computer industry invented an effective solution algorithm, and then there are very good implementation code has been open source for everyone to use, so SVM becomes a benchmark model of classification algorithm. For example, KPCA is a nonlinear dimensionality reduction method proposed by computer science, in fact it is equivalent to classical MDS. The latter is very early in the statistical community, but if there is no new computer industry to discover, some good things may be buried.

Machine learning has now become a major trend in statistics, and many well-known statistical departments have recruited PhD teachers in machine learning fields. Calculations have become more and more important in statistics, and traditional multivariate statistical analysis is based on matrices as computational tools, while modern high-dimensional statistics are optimized as computational tools. On the other hand, the computer discipline offers advanced statistics courses, such as the core curriculum "experience process" in statistics.

Let's look at how machine learning occupies a position in computer science. Recently there is a book that has not yet been published "Foundation of Data Sciences, by Avrim Blum, John Hopcroft, and Ravindran Kannan," one of the authors of John Hopcroft is a Turing Award winner. In the frontier of this book, it is mentioned that the development of computer science can be divided into three stages: early, middle and present. The early days were for computers to work, focusing on developing programming languages, compiling principles, operating systems, and studying mathematical theories that supported them. In the medium term, computers become useful and efficient. The focus is on algorithms and data structures. The third stage is to make the computer more widely used, the development focus from the discrete class of mathematics to the probability and statistics. Then we see that the third stage is actually about machine learning.

Now the computer industry is called machine learning "all-round discipline", it is ubiquitous. On the one hand, machine learning has its own discipline system, on the other hand it also has two important radiation functions. One is to provide the methods and ways to solve the problem for the applied disciplines. In a more popular way, for an applied discipline, the purpose of machine learning is to translate some of the hard-to-understand mathematics into pseudo-code that allows engineers to write programs. Second, for some traditional disciplines, such as statistics, theoretical computer science, logistics optimization, find new research issues.

4, the Enlightenment of machine learning development

The evolution of machine learning tells us that developing a discipline requires a pragmatic approach. The fashionable concept and the name undoubtedly have certain impetus to the popularization of the subject, but the fundamental of the subject is the question, method, technology and foundation of support, as well as the value of the society.

Machine learning is a cool name, simply literally, and its purpose is to make machines capable of learning like humans. But what we have seen before, in its 10 years of golden development, the machine learning community has not too much hype "intelligence", but more attention to the introduction of statistics to establish the theoretical basis of the subject, for data analysis and processing, unsupervised learning and supervised learning as two major research issues, proposed and developed a series of models , methods and computational algorithms, and so on, to effectively solve some practical problems faced by industry. In recent years, due to big data driving and computing ability greatly improved, a number of machine learning for the underlying architecture has been developed, the strong rise of deep neural network to the industry has brought profound changes and opportunities.

The development of machine learning also explains the importance and necessity of interdisciplinary cross-disciplinary. However, this crossover is not simple to know a few nouns or concepts can be, it is necessary to really melt through. Professor Mike Jordan is a first-class computer science and a first-rate statistician, so he can take on the task of building statistical machine learning. And he is very pragmatic, never mention those empty concepts and frameworks. He follows the bottom-up approach, which begins with specific problems, models, methods, algorithms, and then systematically. Professor Geoffrey Hinton is the world's most famous cognitive psychologist and computer science historian. Although he was a very early success in academia, he has a reputation for excellence, but he has been active on the line, writing code. Many of his ideas are simple, workable and very effective, so they are called great thinkers. It is because of his wisdom and the progress of deep learning technology ushered in a revolutionary breakthrough.

The subject of machine learning is also compatible and accepted. We can say that machine learning is created by the forces of academia, industry, entrepreneurship (or competition). Academia is the engine, industry is the driver, the industry is the vitality and the future. Academia and industry should have their own responsibilities and division of labour. The role of academia is to establish and develop machine learning disciplines and to train specialists in the field of machine learning, while large and large projects should be driven by the market and implemented and completed by industry.

5. Development status at home and abroad  

Let's take a look at the current development of machine learning in the world. I mainly look at the situation of several famous universities. At Berkeley, a thought-provoking initiative is that machine learning professors have formal positions in both computer science and statistics, and as far as I know, they are not part-time, and they have the task of teaching courses and research in two departments. Berkeley is the birthplace of statistics in the United States, can be said to be the Holy Land of statistics today, but she is inclusive, not complacent. Professor Mike Jordan is a major creator and catalyst of statistical machine learning, and he has cultivated a large number of outstanding students in the field of machine learning. The Director of the Department of Statistics is now Mike, but his early education has no statistical or mathematical background. It can be said that Berkeley's statistical system has made Mike, and in turn he has created new vitality for Berkeley's statistical development, creating irreplaceable feats.

The Stanford and Berkeley statistics are the two best known in the world. We see that the main direction of the Stanford Statistical Department is statistical learning, such as the Elements of statistical learning that we know is written by several prominent professors of the Department of Statistics. Stanford computer science has been dominated by AI in the world, especially in uncertain reasoning, probabilistic mapping models, probabilistic robots and other fields of achievement, their network of public lessons "machine learning", "Probability map Model" and "artificial intelligence" and so on to benefit the world.

CMU is a very unique school and she is not an American traditional Ivy League university. It can be said that it is based on computer science, it is the world's first establishment of machine learning Department of the school. Professor Mitchell, one of the early creators and guardians of Machine learning, has been teaching machine learning for undergraduates at the university. However, the school is also statistically strong, and in particular, she is the center of the World Study of Bayesian statistics.

In the field of machine learning, the University of Toronto has a pivotal position, and their machine learning team has gathered a number of world-class academics, and it is rare to publish multiple papers in "Science" and "Nature". Professor Geoffrey Hinton is a great thinker, but also a practitioner. He is one of the creators of neural networks and is a major contributor to BP algorithms and deep learning. It is because of his tireless efforts, the neural network ushered in a big outbreak. Professor Radford Neal is a Hinton student who has made a series of important work in the area of Bayesian statistics, especially on MCMC.

International development Status

So let's take a look at the domestic situation. In general, the two disciplines of statistics and computer science are in the early stages of fighting each other, which Larry says. The intersection of statistics and computer science for big data is both an opportunity and a challenge.

I have previously participated in the establishment of the center of Statistical Interdisciplinary Discipline at Zhejiang University, and thus have some knowledge of the statistical community. Statistics in China should still be a weak subject, only recently by the state as a first-class discipline. China's statistics in two extreme, first, it is used as a branch of mathematics, the main research probability theory, stochastic process and mathematical statistics theory. Second, it is divided into the branch of economics, the main research on the application of economic analysis. Machine learning has not been deeply concerned in the statistical field. As a result, deep integration of it and statistics for data processing and analysis has great potential.

Although, I did not with the domestic machine learning or artificial intelligence academia have in-depth contact, but I work in the domestic computer department for nearly 8 years, has been engaged in machine learning related teaching and research, should have a certain say in the status of machine learning. Machine learning in China has received a wide range of attention, but also achieved certain results, but I think high-quality research results are scarce. Enthusiastic about the advanced stage of machine learning some conceptual speculation, they usually do not have much enforceability, preference for large projects, large integration, these should be carried out by the industry, and the theory, methods and other basic research is not taken seriously, the theory is not useful to the point of view is also a great market.

The training system of computer discipline still basically stays in its early development stage. Most schools offer courses in artificial intelligence and machine learning, but both the depth and the frontier lag behind the development of disciplines and cannot meet the needs of the times. The cultivation of talents can not meet the needs of industry, no matter the quality and quantity. This is also the domestic IT company and the international similar companies have a large gap in the technology of the key reasons.

Part II: A few simple research ideas

In this part, my focus goes back to the study of machine learning itself. Machine learning is extensive, and new methods and technologies are being presented and discovered. Here, I try to use the concepts of "multilevel", "adaptive" and "average" to simplify the research ideas and ideas behind the numerous and colorful machine learning models and computational methods. Hopefully, this will inspire you to understand some of the models, methods, and future research that machine learning already has.

1. Multilevel (hierarchical)

First of all, let us focus on the "multilevel" this technical thought. Let's take a look at three specific examples.

The first example is the implicit data model, which is a multilevel model. As an extension of probabilistic graph model, the implicit data model is a kind of important multivariate data analysis method. The implied variable has three important properties. First, it is possible to replace strong boundary independent correlations with weaker conditional independent correlations. The famous de Finetti representation theorem supports this. This theorem says that a set of random variables that can be exchanged can be represented as a mixture of conditional random variables, if and only if they are given in a certain parameter condition. This gives a multilevel representation of a set of random variables that can be exchanged. That is, a parameter is drawn from a distribution, and the set of random variables is extracted independently from a distribution based on this parameter. Second, it can be conveniently calculated by introducing the techniques of implicit variables, such as the desired maximum algorithm and the more generalized data expansion technique. In particular, some complex distributions, such as t-distribution, Laplace distribution can be simplified by means of a Gaussian-scale mixture. Thirdly, the implied variable itself may have some physical meaning that can be explained, which coincides with the application scenario. For example, in an implicit Dirichlet distribution (LDA) model, where the implied variable has the meaning of a subject.

The first example is the implicit data model, which is a multilevel model. As an extension of probabilistic graph model, the implicit data model is a kind of important multivariate data analysis method. The implied variable has three important properties. First, it is possible to replace strong boundary independent correlations with weaker conditional independent correlations. The famous de Finetti representation theorem supports this. This theorem says that a set of random variables that can be exchanged can be represented as a mixture of conditional random variables, if and only if they are given in a certain parameter condition. This gives a multilevel representation of a set of random variables that can be exchanged. That is, a parameter is drawn from a distribution, and the set of random variables is extracted independently from a distribution based on this parameter. Second, it can be conveniently calculated by introducing the techniques of implicit variables, such as the desired maximum algorithm and the more generalized data expansion technique. In particular, some complex distributions, such as t-distribution, Laplace distribution can be simplified by means of a Gaussian-scale mixture. Thirdly, the implied variable itself may have some physical meaning that can be explained, which coincides with the application scenario. For example, in an implicit Dirichlet distribution (LDA) model, where the implied variable has the meaning of a subject.

Laten Dirichlet Allocation

In the second example, we look at the multilevel Bayesian model. In the case of MCMC sampling, the topmost parameters always need to be given first, naturally, the convergence performance of the MCMC algorithm is dependent on these given hyper-parameters, if we have no good experience in the selection of these parameters, then one possible way we add another layer, The higher the number of layers, the more dependent on the hyper-parameter selection.

Hierarchical Bayesian Model

In the third example, deep learning is a multi-level idea. If all the nodes are flattened and then fully connected, it is a fully connected graph. And the CNN depth network can be regarded as a structure regularization of the whole connection graph. Regularization theory is a very central idea of statistical learning. CNN and RNN are two deep neural network models, which are mainly used in image processing and natural language processing respectively. The research shows that the multilevel structure has stronger learning ability.

Deep learning

2. Adaptive (Adaptive)

Let's look at adapting to this technique, and we'll take a few examples to see how this idea works.

The first example is the adaptive critical sampling technique. Important sampling methods generally improve the performance of uniform sampling, while self-adaptation can further improve the performance of important samples.

The second example is the Adaptive column selection problem. Given a matrix A, we want to select some of the columns to form a matrix C, and then use Cc^+a to approximate the original matrix A, and hope that the approximate error is as small as possible. This is a NP-hard problem. In fact, a very small part of the c_1 can be produced by a self-adapting method, which constructs a residual error, defines a probability by this, and then uses the probability to pick up part of the c_2, C_1 and c_2 together to form C.

The third example is an adaptive random iterative algorithm. Considering a minimum empirical risk problem with regularization, when the training data is very long, batch processing is computationally time-consuming, so a random approach is usually used. The existing stochastic gradient or stochastic dual gradient algorithm can obtain an unbiased estimation of the parameters. By introducing adaptive techniques, the estimated variance can be reduced.

A fourth example is the boosting classification method. It adaptively adjusts the weights of each sample, specifically, increases the weight of the divided sample, and reduces the weight of the sample.

3. Average (averaging)

In fact, boosting contains the average thought, that is, I want to talk about the technical ideas. Simply put, boosting is a group of weak classifiers that are integrated together to form a strong classifier. The first benefit is that the risk of fitting can be reduced. Second, you can reduce the risk of falling into the local. Thirdly, the hypothetical space can be extended. Bagging is also a classic integrated learning algorithm that divides training data into groups and then trains the models on small datasets to combine strong classifiers with these models. In addition, this is a two-layer integrated learning approach.

The Classical Anderson acceleration technique is achieved by averaging the idea of accelerating the convergence process. Specifically, it is an overlay process, and this superposition process minimizes a weighted combination by solving a residual error. The advantage of this technique is that it does not add too many calculations, and often can make the numerical iterations more stable.

Another example of using an average is distributed computing. In many cases, distributed computing is not synchronous, asynchronous, and what if it is asynchronous? The simplest is to do it independently, and at some point distribute all the results on average, distributing them to each worker and then running independently, and so on. It's like a hot-start process.

As we have seen, these ideas are often used together, such as the boosting model. Our multi-level, self-adapting and peaceful ideas are straightforward, but indeed useful.

In the Alphago and Li Shishi nine-part chess, a notable detail is that the British flag is hoisted on behalf of the Alpha go side. We know that Alphago was developed by the Deep Mind Team, a British company, but later acquired by Google. Scientific achievements are the wealth shared and shared by the people of the world, but scientists have their national feelings and sense of belonging.

Bit low dare not forget the spring and autumn, I think the fundamental way of development of AI lies in education. Sages said: "Ax." Only by cultivating a batch of mathematical foundation and a strong computer-based hands-on execution, there is a real fusion of cross-cutting ability and international vision of talent, we will have a big act.

Acknowledgements

The above is based on my recent two lectures at the Ninth China R Language Conference (http://china-r.org/bj2016/) and Shanghai Jiaotong University, and in particular the students of the R-Organizer's statistical capital helped me to make a record of the speech. Thanks to the aerclouds of statistics, Lingbing and the invitation of Xiangyu, they and the partners of the statistical capital are doing a meaningful and far-reaching academic public interest, and your feelings and devotion have given me the confidence to openly proclaim my true knowledge and thoughts over the years. Thanks to my students for helping me prepare this lecture report, from the selection of topics, the selection of content, the collection of materials and the production of slides they all gave me great support, and more importantly, they let me in the field of machine learning has been not lonely. Thank you!

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Professor Zhang Zhihua: machine learning--a love of statistics and computation