Dr. Erin LeDell, Machine Learning Scientist, H2O.ai at MLconf SEA - 5/20/16MLconf
Multi-algorithm Ensemble Learning at Scale: Software, Hardware and Algorithmic Approaches: Multi-algorithm ensemble machine learning methods are often used when the true prediction function is not easily approximated by a single algorithm. The Super Learner algorithm, also known as stacking, combines multiple, typically diverse, base learning algorithms into a single, powerful prediction function through a secondary learning process called metalearning. Although ensemble methods offer superior performance over their singleton counterparts, there is an implicit computational cost to ensembles, as it requires training and cross-validating multiple base learning algorithms.
We will demonstrate a variety of software- and hardware-based approaches that lead to more scalable ensemble learning software, including a highly scalable implementation of stacking called “H2O Ensemble”, built on top of the open source, distributed machine learning platform, H2O. H2O Ensemble scales across multi-node clusters and allows the user to create ensembles of deep neural networks, Gradient Boosting Machines, Random Forest, and others. As for algorithm-based approaches, we will present two algorithmic modifications to the original stacking algorithm that further reduce computation time — Subsemble algorithm and the Online Super Learner algorithm. This talk will also include benchmarks of the implementations of these new stacking variants.
Dr. Erin LeDell, Machine Learning Scientist, H2O.ai at MLconf SEA - 5/20/16MLconf
Multi-algorithm Ensemble Learning at Scale: Software, Hardware and Algorithmic Approaches: Multi-algorithm ensemble machine learning methods are often used when the true prediction function is not easily approximated by a single algorithm. The Super Learner algorithm, also known as stacking, combines multiple, typically diverse, base learning algorithms into a single, powerful prediction function through a secondary learning process called metalearning. Although ensemble methods offer superior performance over their singleton counterparts, there is an implicit computational cost to ensembles, as it requires training and cross-validating multiple base learning algorithms.
We will demonstrate a variety of software- and hardware-based approaches that lead to more scalable ensemble learning software, including a highly scalable implementation of stacking called “H2O Ensemble”, built on top of the open source, distributed machine learning platform, H2O. H2O Ensemble scales across multi-node clusters and allows the user to create ensembles of deep neural networks, Gradient Boosting Machines, Random Forest, and others. As for algorithm-based approaches, we will present two algorithmic modifications to the original stacking algorithm that further reduce computation time — Subsemble algorithm and the Online Super Learner algorithm. This talk will also include benchmarks of the implementations of these new stacking variants.
Le Song, Assistant Professor, College of Computing, Georgia Institute of Tech...MLconf
Understanding Deep Learning for Big Data: The complexity and scale of big data impose tremendous challenges for their analysis. Yet, big data also offer us great opportunities. Some nonlinear phenomena, features or relations, which are not clear or cannot be inferred reliably from small and medium data, now become clear and can be learned robustly from big data. Typically, the form of the nonlinearity is unknown to us, and needs to be learned from data as well. Being able to harness the nonlinear structures from big data could allow us to tackle problems which are impossible before or obtain results which are far better than previous state-of-the-arts.
Nowadays, deep neural networks are the methods of choice when it comes to large scale nonlinear learning problems. What makes deep neural networks work? Is there any general principle for tackling high dimensional nonlinear problems which we can learn from deep neural works? Can we design competitive or better alternatives based on such knowledge? To make progress in these questions, my machine learning group performed both theoretical and experimental analysis on existing and new deep learning architectures, and investigate three crucial aspects on the usefulness of the fully connected layers, the advantage of the feature learning process, and the importance of the compositional structures. Our results point to some promising directions for future research, and provide guideline for building new deep learning models.
Melanie Warrick, Deep Learning Engineer, Skymind.io at MLconf SF - 11/13/15MLconf
Attention Neural Net Model Fundamentals: Neural networks have regained popularity over the last decade because they are demonstrating real world value in different applications (e.g. targeted advertising, recommender engines, Siri, self driving cars, facial recognition). Several model types are currently explored in the field with recurrent neural networks (RNN) and convolution neural networks (CNN) taking the top focus. The attention model, a recently developed RNN variant, has started to play a larger role in both natural language processing and image analysis research.
This talk will cover the fundamentals of the attention model structure and how its applied to visual and speech analysis. I will provide an overview of the model functionality and math including a high-level differentiation between soft and hard types. The goal is to give you enough of an understanding of what the model is, how it works and where to apply it.
Josh Patterson, Principal at Patterson Consulting: Introduction to Parallel Iterative Machine Learning Algorithms on Hadoop’s NextGeneration YARN Framework
Sergei Vassilvitskii, Research Scientist, Google at MLconf NYC - 4/15/16MLconf
Teaching K-Means New Tricks: Over 50 years old, the k-means algorithm remains one of the most popular clustering algorithms. In this talk we’ll cover some recent developments, including better initialization, the notion of coresets, clustering at scale, and clustering with outliers.
Corinna Cortes, Head of Research, Google, at MLconf NYC 2017MLconf
Corinna Cortes is a Danish computer scientist known for her contributions to machine learning. She is currently the Head of Google Research, New York. Cortes is a recipient of the Paris Kanellakis Theory and Practice Award for her work on theoretical foundations of support vector machines.
Cortes received her M.S. degree in physics from Copenhagen University in 1989. In the same year she joined AT&T Bell Labs as a researcher and remained there for about ten years. She received her Ph.D. in computer science from the University of Rochester in 1993. Cortes currently serves as the Head of Google Research, New York. She is an Editorial Board member of the journal Machine Learning.
Cortes’ research covers a wide range of topics in machine learning, including support vector machines and data mining. In 2008, she jointly with Vladimir Vapnik received the Paris Kanellakis Theory and Practice Award for the development of a highly effective algorithm for supervised learning known as support vector machines (SVM). Today, SVM is one of the most frequently used algorithms in machine learning, which is used in many practical applications, including medical diagnosis and weather forecasting.
Abstract Summary:
Harnessing Neural Networks:
Deep learning has demonstrated impressive performance gain in many machine learning applications. However, unveiling and realizing these performance gains is not always straightforward. Discovering the right network architecture is critical for accuracy and often requires a human in the loop. Some network architectures occasionally produce spurious outputs, and the outputs have to be restricted to meet the needs of an application. Finally, realizing the performance gain in a production system can be difficult because of extensive inference times.
In this talk we discuss methods for making neural networks efficient in production systems. We also discuss an efficient method for automatically learning the network architecture, called AdaNet. We provide theoretical arguments for the algorithm and present experimental evidence for its effectiveness.
Slides from the presentation given at M^3 conference: http://www.mcubed.london/
The idea is to use 3 statements to describe and start to work with the TensorFlow library.
https://telecombcn-dl.github.io/2017-dlai/
Deep learning technologies are at the core of the current revolution in artificial intelligence for multimedia data analysis. The convergence of large-scale annotated datasets and affordable GPU hardware has allowed the training of neural networks for data analysis tasks which were previously addressed with hand-crafted features. Architectures such as convolutional neural networks, recurrent neural networks or Q-nets for reinforcement learning have shaped a brand new scenario in signal processing. This course will cover the basic principles of deep learning from both an algorithmic and computational perspectives.
Interaction Networks for Learning about Objects, Relations and PhysicsKen Kuroki
For my presentation for a reading group. I have not in any way contributed this study, which is done by the researchers named on the first slide.
https://papers.nips.cc/paper/6418-interaction-networks-for-learning-about-objects-relations-and-physics
Accelerating Random Forests in Scikit-LearnGilles Louppe
Random Forests are without contest one of the most robust, accurate and versatile tools for solving machine learning tasks. Implementing this algorithm properly and efficiently remains however a challenging task involving issues that are easily overlooked if not considered with care. In this talk, we present the Random Forests implementation developed within the Scikit-Learn machine learning library. In particular, we describe the iterative team efforts that led us to gradually improve our codebase and eventually make Scikit-Learn's Random Forests one of the most efficient implementations in the scientific ecosystem, across all libraries and programming languages. Algorithmic and technical optimizations that have made this possible include:
- An efficient formulation of the decision tree algorithm, tailored for Random Forests;
- Cythonization of the tree induction algorithm;
- CPU cache optimizations, through low-level organization of data into contiguous memory blocks;
- Efficient multi-threading through GIL-free routines;
- A dedicated sorting procedure, taking into account the properties of data;
- Shared pre-computations whenever critical.
Overall, we believe that lessons learned from this case study extend to a broad range of scientific applications and may be of interest to anybody doing data analysis in Python.
MS CS - Selecting Machine Learning AlgorithmKaniska Mandal
ML Algorithms usually solve an optimization problem such that we need to find parameters for a given model that minimizes
— Loss function (prediction error)
— Model simplicity (regularization)
https://telecombcn-dl.github.io/2018-dlai/
Deep learning technologies are at the core of the current revolution in artificial intelligence for multimedia data analysis. The convergence of large-scale annotated datasets and affordable GPU hardware has allowed the training of neural networks for data analysis tasks which were previously addressed with hand-crafted features. Architectures such as convolutional neural networks, recurrent neural networks or Q-nets for reinforcement learning have shaped a brand new scenario in signal processing. This course will cover the basic principles of deep learning from both an algorithmic and computational perspectives.
Le Song, Assistant Professor, College of Computing, Georgia Institute of Tech...MLconf
Understanding Deep Learning for Big Data: The complexity and scale of big data impose tremendous challenges for their analysis. Yet, big data also offer us great opportunities. Some nonlinear phenomena, features or relations, which are not clear or cannot be inferred reliably from small and medium data, now become clear and can be learned robustly from big data. Typically, the form of the nonlinearity is unknown to us, and needs to be learned from data as well. Being able to harness the nonlinear structures from big data could allow us to tackle problems which are impossible before or obtain results which are far better than previous state-of-the-arts.
Nowadays, deep neural networks are the methods of choice when it comes to large scale nonlinear learning problems. What makes deep neural networks work? Is there any general principle for tackling high dimensional nonlinear problems which we can learn from deep neural works? Can we design competitive or better alternatives based on such knowledge? To make progress in these questions, my machine learning group performed both theoretical and experimental analysis on existing and new deep learning architectures, and investigate three crucial aspects on the usefulness of the fully connected layers, the advantage of the feature learning process, and the importance of the compositional structures. Our results point to some promising directions for future research, and provide guideline for building new deep learning models.
Melanie Warrick, Deep Learning Engineer, Skymind.io at MLconf SF - 11/13/15MLconf
Attention Neural Net Model Fundamentals: Neural networks have regained popularity over the last decade because they are demonstrating real world value in different applications (e.g. targeted advertising, recommender engines, Siri, self driving cars, facial recognition). Several model types are currently explored in the field with recurrent neural networks (RNN) and convolution neural networks (CNN) taking the top focus. The attention model, a recently developed RNN variant, has started to play a larger role in both natural language processing and image analysis research.
This talk will cover the fundamentals of the attention model structure and how its applied to visual and speech analysis. I will provide an overview of the model functionality and math including a high-level differentiation between soft and hard types. The goal is to give you enough of an understanding of what the model is, how it works and where to apply it.
Josh Patterson, Principal at Patterson Consulting: Introduction to Parallel Iterative Machine Learning Algorithms on Hadoop’s NextGeneration YARN Framework
Sergei Vassilvitskii, Research Scientist, Google at MLconf NYC - 4/15/16MLconf
Teaching K-Means New Tricks: Over 50 years old, the k-means algorithm remains one of the most popular clustering algorithms. In this talk we’ll cover some recent developments, including better initialization, the notion of coresets, clustering at scale, and clustering with outliers.
Corinna Cortes, Head of Research, Google, at MLconf NYC 2017MLconf
Corinna Cortes is a Danish computer scientist known for her contributions to machine learning. She is currently the Head of Google Research, New York. Cortes is a recipient of the Paris Kanellakis Theory and Practice Award for her work on theoretical foundations of support vector machines.
Cortes received her M.S. degree in physics from Copenhagen University in 1989. In the same year she joined AT&T Bell Labs as a researcher and remained there for about ten years. She received her Ph.D. in computer science from the University of Rochester in 1993. Cortes currently serves as the Head of Google Research, New York. She is an Editorial Board member of the journal Machine Learning.
Cortes’ research covers a wide range of topics in machine learning, including support vector machines and data mining. In 2008, she jointly with Vladimir Vapnik received the Paris Kanellakis Theory and Practice Award for the development of a highly effective algorithm for supervised learning known as support vector machines (SVM). Today, SVM is one of the most frequently used algorithms in machine learning, which is used in many practical applications, including medical diagnosis and weather forecasting.
Abstract Summary:
Harnessing Neural Networks:
Deep learning has demonstrated impressive performance gain in many machine learning applications. However, unveiling and realizing these performance gains is not always straightforward. Discovering the right network architecture is critical for accuracy and often requires a human in the loop. Some network architectures occasionally produce spurious outputs, and the outputs have to be restricted to meet the needs of an application. Finally, realizing the performance gain in a production system can be difficult because of extensive inference times.
In this talk we discuss methods for making neural networks efficient in production systems. We also discuss an efficient method for automatically learning the network architecture, called AdaNet. We provide theoretical arguments for the algorithm and present experimental evidence for its effectiveness.
Slides from the presentation given at M^3 conference: http://www.mcubed.london/
The idea is to use 3 statements to describe and start to work with the TensorFlow library.
https://telecombcn-dl.github.io/2017-dlai/
Deep learning technologies are at the core of the current revolution in artificial intelligence for multimedia data analysis. The convergence of large-scale annotated datasets and affordable GPU hardware has allowed the training of neural networks for data analysis tasks which were previously addressed with hand-crafted features. Architectures such as convolutional neural networks, recurrent neural networks or Q-nets for reinforcement learning have shaped a brand new scenario in signal processing. This course will cover the basic principles of deep learning from both an algorithmic and computational perspectives.
Interaction Networks for Learning about Objects, Relations and PhysicsKen Kuroki
For my presentation for a reading group. I have not in any way contributed this study, which is done by the researchers named on the first slide.
https://papers.nips.cc/paper/6418-interaction-networks-for-learning-about-objects-relations-and-physics
Accelerating Random Forests in Scikit-LearnGilles Louppe
Random Forests are without contest one of the most robust, accurate and versatile tools for solving machine learning tasks. Implementing this algorithm properly and efficiently remains however a challenging task involving issues that are easily overlooked if not considered with care. In this talk, we present the Random Forests implementation developed within the Scikit-Learn machine learning library. In particular, we describe the iterative team efforts that led us to gradually improve our codebase and eventually make Scikit-Learn's Random Forests one of the most efficient implementations in the scientific ecosystem, across all libraries and programming languages. Algorithmic and technical optimizations that have made this possible include:
- An efficient formulation of the decision tree algorithm, tailored for Random Forests;
- Cythonization of the tree induction algorithm;
- CPU cache optimizations, through low-level organization of data into contiguous memory blocks;
- Efficient multi-threading through GIL-free routines;
- A dedicated sorting procedure, taking into account the properties of data;
- Shared pre-computations whenever critical.
Overall, we believe that lessons learned from this case study extend to a broad range of scientific applications and may be of interest to anybody doing data analysis in Python.
MS CS - Selecting Machine Learning AlgorithmKaniska Mandal
ML Algorithms usually solve an optimization problem such that we need to find parameters for a given model that minimizes
— Loss function (prediction error)
— Model simplicity (regularization)
https://telecombcn-dl.github.io/2018-dlai/
Deep learning technologies are at the core of the current revolution in artificial intelligence for multimedia data analysis. The convergence of large-scale annotated datasets and affordable GPU hardware has allowed the training of neural networks for data analysis tasks which were previously addressed with hand-crafted features. Architectures such as convolutional neural networks, recurrent neural networks or Q-nets for reinforcement learning have shaped a brand new scenario in signal processing. This course will cover the basic principles of deep learning from both an algorithmic and computational perspectives.
Simple representations for learning: factorizations and similarities Gael Varoquaux
Real-life data seldom comes in the ideal form for statistical learning.
This talk focuses on high-dimensional problems for signals and
discrete entities: when dealing with many, correlated, signals or
entities, it is useful to extract representations that capture these
correlations.
Matrix factorization models provide simple but powerful representations. They are used for recommender systems across discrete entities such as users and products, or to learn good dictionaries to represent images. However they entail large computing costs on very high-dimensional data, databases with many products or high-resolution images. I will present an
algorithm to factorize huge matrices based on stochastic subsampling that gives up to 10-fold speed-ups [1].
With discrete entities, the explosion of dimensionality may be due to variations in how a smaller number of categories are represented. Such a problem of "dirty categories" is typical of uncurated data sources. I will discuss how encoding this data based on similarities recovers a useful category structure with no preprocessing. I will show how it interpolates between one-hot encoding and techniques used in character-level natural language processing.
[1] Stochastic subsampling for factorizing huge matrices, A Mensch, J Mairal, B Thirion, G Varoquaux, IEEE Transactions on Signal Processing 66 (1), 113-128
[2] Similarity encoding for learning with dirty categorical variables. P Cerda, G Varoquaux, B Kégl Machine Learning (2018): 1-18
Machine learning in science and industry — day 1arogozhnikov
A course of machine learning in science and industry.
- notions and applications
- nearest neighbours: search and machine learning algorithms
- roc curve
- optimal classification and regression
- density estimation
- Gaussian mixtures and EM algorithm
- clustering, an example of clustering in the opera
Slides for the presentation at ENBIS 2018 of "Deep k-Means: Jointly Clustering with k-Means and Learning Representations" by Thibaut Thonet. Joint work with Maziar Moradi Fard and Eric Gaussier.
Automatic Task-based Code Generation for High Performance DSELJoel Falcou
Providing high level tools for parallel programming while sustaining a high level of performance has been a challenge that techniques like Domain Specific Embedded Languages try to solve. In previous works, we investigated the design of such a DSEL – NT2 – providing a Matlab -like syntax for parallel numerical computations inside a C++ library.
Main issues addressed here is how liimtaions of classical DSEL generation and multithreaded code generation can be overcome.
Imagine writing a pure Python library which can achieve the performance of Fortran or C/C++.
To this end we have developed Pyccel, which translates Python code to either Fortran or C, and makes the generated code callable from Python. The generated Fortran or C code is not only fast, but also human-readable; hence it can easily be profiled and optimized for the target machine.
Pyccel has a focus on high-performance computing applications, where the efficient usage of the available hardware resources is fundamental.
To this end it provides type annotations, function decorators, and OpenMP pragmas.
Pyccel is easy to use, is almost completely written in Python, and compares favourably against other Python accelerators.
Learning to rank (LTR) for information retrieval (IR) involves the application of machine learning models to rank artifacts, such as webpages, in response to user's need, which may be expressed as a query. LTR models typically employ training data, such as human relevance labels and click data, to discriminatively train towards an IR objective. The focus of this lecture will be on the fundamentals of neural networks and their applications to learning to rank.
WISS 2015 - Machine Learning lecture by Ludovic Samper Antidot
Machine Learning Tutorial
- Study a classical task in Machine Learning : text classification - - Show scikit-learn.org Python machine learning library
- Follow the “Working with text data” tutorial :
http://scikit-learn.org/stable/tutorial/text_analytics/ working_with_text_data.html
- Additional material on http://blog.antidot.net/
Similar to Massive Matrix Factorization : Applications to collaborative filtering (20)
A brief information about the SCOP protein database used in bioinformatics.
The Structural Classification of Proteins (SCOP) database is a comprehensive and authoritative resource for the structural and evolutionary relationships of proteins. It provides a detailed and curated classification of protein structures, grouping them into families, superfamilies, and folds based on their structural and sequence similarities.
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Comparing Evolved Extractive Text Summary Scores of Bidirectional Encoder Rep...University of Maribor
Slides from:
11th International Conference on Electrical, Electronics and Computer Engineering (IcETRAN), Niš, 3-6 June 2024
Track: Artificial Intelligence
https://www.etran.rs/2024/en/home-english/
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Cell utilize energy in the form of ATP.
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introduction to WARBERG PHENOMENA:
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Otto Heinrich Warburg (; 8 October 1883 – 1 August 1970) In 1931 was awarded the Nobel Prize in Physiology for his "discovery of the nature and mode of action of the respiratory enzyme.
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The ASGCT Annual Meeting was packed with exciting progress in the field advan...
Massive Matrix Factorization : Applications to collaborative filtering
1. Dictionary Learning for
Massive Matrix Factorization
Arthur Mensch, Julien Mairal
Ga¨el Varoquaux, Bertrand Thirion
Inria Parietal, Inria Thoth
October 6, 2016
2. Introduction
Why am I here ?
Inria Parietal: machine learning for neuro-imaging
(fMRI data)
Matrix factorization: major ingredient in fMRI analysis
Very large datasets (2 TB): we designed faster algorithms
These algorithms can be used in collaborative filtering
D AX
Voxels
Time
=
k spatial maps Time
x
1
Work presented at ICML 2016
Arthur Mensch Dictionary Learning for Massive Matrix Factorization 1 / 28
3. D´eroul´e
1 Matrix factorization for recommender systems
Collaborative filtering
Matrix factorization formulation
Existing methods
2 Subsampled online dictionary learning
Dictionary learning – existing methods
Handling missing values efficiently
New algorithm
3 Results
Setting
Benchmarks
Parameter setting
Arthur Mensch Dictionary Learning for Massive Matrix Factorization 2 / 28
4. D´eroul´e
1 Matrix factorization for recommender systems
Collaborative filtering
Matrix factorization formulation
Existing methods
2 Subsampled online dictionary learning
Dictionary learning – existing methods
Handling missing values efficiently
New algorithm
3 Results
Setting
Benchmarks
Parameter setting
Arthur Mensch Dictionary Learning for Massive Matrix Factorization 3 / 28
5. Collaborative filtering
Collaborative platform
n users rate a fraction of
p items
e.g movies, restaurants
Estimate ratings for
recommendation
Use the ratings of other users for recommendation
Arthur Mensch Dictionary Learning for Massive Matrix Factorization 4 / 28
6. How to predict ratings ?
Credit: [Bell and Koren, 2007]
Joe like We were
soldiers, Black Hawk
down.
Bob and Alice like the
same films, and also
like Saving private
Ryan.
Joe should watch
Saving private Ryan,
because all of them
indeed likes war films.
Need to uncover topics in items
Arthur Mensch Dictionary Learning for Massive Matrix Factorization 5 / 28
7. Predicting rate with scalar products
Embeddings to model the existence of genre/category/topics
Representative vectors for
users and items:
(αj
)1≤j≤n, (di )1≤i≤p ∈ Rk
q-th coefficient of di , αj
= affinity with the “topic” q
xij αj
di
k topics
di
αj
1
Arthur Mensch Dictionary Learning for Massive Matrix Factorization 6 / 28
8. Predicting rate with scalar products
Embeddings to model the existence of genre/category/topics
Representative vectors for
users and items:
(αj
)1≤j≤n, (di )1≤i≤p ∈ Rk
q-th coefficient of di , αj
= affinity with the “topic” q
Ratings xij (item i, user j):
xij = di αj
( + biases)
= Common affinity for topics
xij αj
di
k topics
di
αj
1
Arthur Mensch Dictionary Learning for Massive Matrix Factorization 6 / 28
9. Predicting rate with scalar products
Embeddings to model the existence of genre/category/topics
Representative vectors for
users and items:
(αj
)1≤j≤n, (di )1≤i≤p ∈ Rk
q-th coefficient of di , αj
= affinity with the “topic” q
Ratings xij (item i, user j):
xij = di αj
( + biases)
= Common affinity for topics
xij αj
di
k topics
di
αj
1
Learning problem: estimate D and A with known ratings
Arthur Mensch Dictionary Learning for Massive Matrix Factorization 6 / 28
10. Matrix factorization
1Ω X AD
p
n k
n
=
1
X ∈ Rp×n ≈ DA ∈ Rp×k × Rk×n
Constraints / penalty on factors D and A
We only observe 1Ω X — Ω set of ratings provided by users
Recommender systems : millions of users, millions of items
How to scale matrix factorization to very large datasets ?
Arthur Mensch Dictionary Learning for Massive Matrix Factorization 7 / 28
11. Formalism
Finding representation in Rk for items and users:
min
D∈Rp×k
A∈Rk×n (i,j)∈Ω
(xij − di αj
)2
+ λ( D 2
F + A 2
F )
= 1Ω (X − DA) 2
2 + λ( D 2
F + A 2
F ) 1Ω set of knownratings
2 reconstruction loss — 2 penalty for generalization
Existing methods
Alternated minimization
Stochastic gradient descent
Arthur Mensch Dictionary Learning for Massive Matrix Factorization 8 / 28
12. Existing methods
Alternated minimization
Minimize over A, D: alternate between
D = min
D∈Rp×k
(i,j)∈Ω
(xij − di αj
)2
+ λ D 2
F
A = min
A∈Rk×n
(i,j)∈Ω
(xij − di αj
)2
+ λ A 2
F
No hyperparameters
Slow and memory expensive: use all ratings at each iteration
a.k.a. coordinate descent (variation in parameter update order)
Arthur Mensch Dictionary Learning for Massive Matrix Factorization 9 / 28
13. Existing methods
Stochastic gradient descent
min
A,D
(i,j)∈Ω
fij (A, B)
def
= (xij − di αj
)2
+
1
cj
λ αj 2
2 +
1
ci
λ di
2
2
Gradient step for each rating:
(At, Dt) ← (At−1, Dt−1)−
1
ct
(A,D)fij (At−1, Dt−1)
Fast and memory efficient – won the Netflix prize
Very sensitive to step sizes (ct) – need to cross-validate
Arthur Mensch Dictionary Learning for Massive Matrix Factorization 10 / 28
14. Towards a new algorithm
Best of both worlds ?
Fast and memory efficient algorithm
Little sensitive to hyperparameter setting
Subsampled online dictionary learning
Builds upon the online dictionary learning algorithm
popular in computer vision and interpretable learning (fMRI)
Adapt it to handle missing values efficiently
Arthur Mensch Dictionary Learning for Massive Matrix Factorization 11 / 28
15. D´eroul´e
1 Matrix factorization for recommender systems
Collaborative filtering
Matrix factorization formulation
Existing methods
2 Subsampled online dictionary learning
Dictionary learning – existing methods
Handling missing values efficiently
New algorithm
3 Results
Setting
Benchmarks
Parameter setting
Arthur Mensch Dictionary Learning for Massive Matrix Factorization 12 / 28
16. Dictionary learning
Recall: recommender system formalism
Non-masked matrix factorization with 2 penalty:
min
D∈Rp×k
A∈Rk×n
n
j=1
(xj
− D αj
)2
+ λ( D 2
F + A 2
F )
Penalties can be richer, and made into constraints
Dictionary learning
Learn the left side factor [Olshausen and Field, 1997]
min
D∈C
n
j=1
xj
−Dαj 2
2 +λΩ(αj
) αj
= argmin
α∈Rk
xi
−Dα 2
2 +λΩ(α)
Naive approach: alternated minimization
Arthur Mensch Dictionary Learning for Massive Matrix Factorization 13 / 28
17. Online dictionary learning [Mairal et al., 2010]
At iteration t, select xt in {xj }j (user ratings), improve D
Single iteration complexity ∝ sample dimension O(p)
(Dt)t converges in a few epochs (one for large n)
xt αtD
p
n k n
=Stream
1
Very efficient in computer vision / networks / fMRI /
hyperspectral images
Can we use it efficiently for recommender systems ?
Arthur Mensch Dictionary Learning for Massive Matrix Factorization 14 / 28
18. In short: Handling missing values
X
p
n
xt
Steam
Handle large n
n
Handle missing values
Online → online + partial
Batch →
online
Mtxt
Stream
Ignore
Unknown
Unaccessed
1
Leverage streaming + partial access to samples
Arthur Mensch Dictionary Learning for Massive Matrix Factorization 15 / 28
19. In detail: online dictionary learning
Objective function involves latent codes (right side factor)
min
D∈C
1
t
t
i=1
xi − Dα∗
i (D) 2
2, α∗
i (D) = argmin
α
1
2
xi − Dα 2
2 + λΩ(α)
Replace latent codes by codes computed with old dictionaries
Build an upper-bounding surrogate function
min
1
t
t
i=1
xi −Dαi
2
2 αi = argmin
α
1
2
xi −Di−1α 2
2+λΩ(α)
Minimize surrogate — updateable online at low cost
Arthur Mensch Dictionary Learning for Massive Matrix Factorization 16 / 28
20. In detail: online dictionary learning
Algorithm outline
1 Compute code
αt = argmin
α∈Rk
xt − Dt−1α 2
2 + λΩ(αt)
2 Update the surrogate function
gt =
1
t
t
i=1
xi − Dαi
2
2 = Tr (
1
2
D DAt − D Bt)
At = (1 −
1
t
)At−1 +
1
t
αtαt Bt = (1 −
1
t
)Bt−1 +
1
t
xtαt
3 Minimize surrogate
Dt = argmin
D∈C
gt(D) gt = DAt − Bt
Arthur Mensch Dictionary Learning for Massive Matrix Factorization 17 / 28
21. In detail: online dictionary learning
Algorithm outline
1 Compute code – xt → complexity depends on p
αt = argmin
α∈Rk
xt − Dt−1α 2
2 + λΩ(αt)
2 Update the surrogate function – Complexity in O(p)
gt =
1
t
t
i=1
xi − Dαi
2
2 = Tr (
1
2
D DAt − D Bt)
At = (1 −
1
t
)At−1 +
1
t
αtαt Bt = (1 −
1
t
)Bt−1 +
1
t
xtαt
3 Minimize surrogate – Complexity in O(p)
Dt = argmin
D∈C
gt(D) gt = DAt − Bt
Arthur Mensch Dictionary Learning for Massive Matrix Factorization 17 / 28
22. Specification for a new algorithm
Mtxt
Stream
Ignore
p
n
1
Constrained : use only known
ratings from Ω
Efficient: single iteration in O(s),
# of ratings provided by user t
Principled: follows the online
matrix factorization algorithm as
much as possible
Arthur Mensch Dictionary Learning for Massive Matrix Factorization 18 / 28
23. Missing values in practice
Data stream: (xt)t → masked (Mtxt)t
= ratings from user t
Dimension: p (all items) → s (rated items)
Use only Mtxt in algorithm computation
→ complexity in O(s)
Mtxt
Stream
Ignore
p
n
1
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24. Missing values in practice
Data stream: (xt)t → masked (Mtxt)t
= ratings from user t
Dimension: p (all items) → s (rated items)
Use only Mtxt in algorithm computation
→ complexity in O(s)
Mtxt
Stream
Ignore
p
n
1
Adaptation to make
Modify all parts of the algorithm to obtain O(s) complexity
1 Code
computation
2 Surrogate
update
3 Surrogate
minimization
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25. Subsampled online dictionary learning
Check out paper !
Original online MF
1 Code computation
αt = argmin
α∈Rk
xt − Dt−1α 2
2
+ λΩ(αt )
2 Surrogate aggregation
At =
1
t
t
i=1
αi αi
Bt = Bt−1 +
1
t
(xt αt − Bt−1)
3 Surrogate minimization
Dj
← p⊥
Cr
j
(Dj
−
1
(At )j,j
(DAj
t −Bj
t ))
Our algorithm
1 Code computation: masked loss
αt = argmin
α∈Rk
Mt (xt − Dt−1α) 2
2
+ λ
rk Mt
p
Ω(αt )
2 Surrogate aggregation
At =
1
t
t
i=1
αi αi
Bt = Bt−1 +
1
t
i=1 Mi
(Mt xt αt − Mt Bt−1)
3 Surrogate minimization
Mt Dj
← p⊥
Cj
(Mt Dj
−
1
(At )j,j
Mt (D(Aj
t − (Bj
t ))
Arthur Mensch Dictionary Learning for Massive Matrix Factorization 20 / 28
26. D´eroul´e
1 Matrix factorization for recommender systems
Collaborative filtering
Matrix factorization formulation
Existing methods
2 Subsampled online dictionary learning
Dictionary learning – existing methods
Handling missing values efficiently
New algorithm
3 Results
Setting
Benchmarks
Parameter setting
Arthur Mensch Dictionary Learning for Massive Matrix Factorization 21 / 28
27. Experiments
Validation : Test RMSE (rating prediction) vs CPU time
Baseline : Coordinate descent solver [Yu et al., 2012] for
min
D∈Rp×k
A∈Rk×n (i,j)∈Ω
(xij − di αj
)2
+ λ( D 2
F + A 2
F )
Fastest solver available apart from SGD — hyperparameters
↑ Our method has a learning rate with little influence
Datasets : Movielens, Netflix
Publicly available
Larger one in the industry...
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29. Performance
Dataset Test RMSE Convergence time Speed
CD SODL CD SODL -up
ML 1M 0.872 0.866 6 s 8 s ×0.75
ML 10M 0.802 0.799 223 s 60 s ×3.7
NF (140M) 0.938 0.934 1714 s 256 s ×6.8
Outperform coordinate descent beyond 10M ratings
Same prediction performance
Speed-up 6.8× on Netflix
Simple model: RMSE is not state-of-the-art
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30. Robustness to learning rate
Learning rate in algorithm to be set in [0.75, 1] (← theory)
In practice: Just set it in [0.8, 1]
1 10 40Epoch
0.80
0.81
0.82
0.83
0.84
0.85
0.86
0.87
RMSEontestset
Learning rate β0.75
0.78
0.81
0.83
0.86
0.89
0.92
0.94
0.97
1.00
MovieLens 10M
.1 1 10 20
0.93
0.94
0.95
0.96
0.97
0.98
0.99
Netflix
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31. Conclusion
Take-home message
Online matrix factorization can be adapted
to handle missing value efficiently, with very
good performance in reccommender system
Mtxt
Stream
Ignore
p
n
1Algorithm usable in any rich model involving matrix factorization
Python package http://github.com/arthurmensch/modl
Article/slides at http://amensch.fr/publications
Arthur Mensch Dictionary Learning for Massive Matrix Factorization 26 / 28
32. Conclusion
Take-home message
Online matrix factorization can be adapted
to handle missing value efficiently, with very
good performance in reccommender system
Mtxt
Stream
Ignore
p
n
1Algorithm usable in any rich model involving matrix factorization
Python package http://github.com/arthurmensch/modl
Article/slides at http://amensch.fr/publications
Questions ?
Arthur Mensch Dictionary Learning for Massive Matrix Factorization 26 / 28
33. Appendix: Resting-state fMRI
Online dictionary learning
235 h run time
1 full epoch
10 h run time
1
24 epoch
Proposed method
10 h run time
1
2 epoch, reduction r=12
Qualitatively, usable maps are obtained 10× faster
Arthur Mensch Dictionary Learning for Massive Matrix Factorization 27 / 28
34. Bibliography I
[Bell and Koren, 2007] Bell, R. M. and Koren, Y. (2007).
Lessons from the Netflix prize challenge.
ACM SIGKDD Explorations Newsletter, 9(2):75–79.
[Mairal et al., 2010] Mairal, J., Bach, F., Ponce, J., and Sapiro, G. (2010).
Online learning for matrix factorization and sparse coding.
The Journal of Machine Learning Research, 11:19–60.
[Olshausen and Field, 1997] Olshausen, B. A. and Field, D. J. (1997).
Sparse coding with an overcomplete basis set: A strategy employed by V1?
Vision Research, 37(23):3311–3325.
[Yu et al., 2012] Yu, H.-F., Hsieh, C.-J., and Dhillon, I. (2012).
Scalable coordinate descent approaches to parallel matrix factorization for
recommender systems.
In Proceedings of the International Conference on Data Mining, pages
765–774. IEEE.
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