This document presents Principal Sensitivity Analysis (PSA) as a method to summarize and visualize the knowledge learned by machine learning models. PSA identifies the principal directions in the input space that the model is most sensitive to through Principal Sensitivity Maps (PSMs). PSMs can distinguish how different input features characterize different classes. Local sensitivity measures show how PSMs contribute to specific classifications. PSA was demonstrated on a neural network for digit classification, finding that different PSMs helped distinguish different digit pairs. PSA provides insights into machine learning models beyond what is possible with traditional sensitivity analysis.
The Computer Science solves a lot of daily problems in our lifes, one of them is search problems. These problems sometimes are so hard to find a good solution because is necessary study hard to comprehend the problem, modeling it and after this propose a solution. In this homework, my goal is define and explain the differ- ences between the algorithms DFS - Depth-First Search and Backtrancking. Firstly, I will introduce these algorithms in the section 2 and 3 to DFS and Backtracking respectively. In the section 4 I will show the differences between them. Finally, the conclusion in the section 5.
I made this presentation for my class presentation. Sorry if there's some mistakes in my way to explain it... This is about the depth-first search algorithm and this is a paper review...the title of the paper is Self-Stabilizing Depth-First Search
The Computer Science solves a lot of daily problems in our lifes, one of them is search problems. These problems sometimes are so hard to find a good solution because is necessary study hard to comprehend the problem, modeling it and after this propose a solution. In this homework, my goal is define and explain the differ- ences between the algorithms DFS - Depth-First Search and Backtrancking. Firstly, I will introduce these algorithms in the section 2 and 3 to DFS and Backtracking respectively. In the section 4 I will show the differences between them. Finally, the conclusion in the section 5.
I made this presentation for my class presentation. Sorry if there's some mistakes in my way to explain it... This is about the depth-first search algorithm and this is a paper review...the title of the paper is Self-Stabilizing Depth-First Search
Connect-the-Dots in a Graph and Buffon's Needle on a Chessboard: Two Problems...Vladimir Kulyukin
We study two theoretical problems that arise naturally in the application domain of assisted
navigation. Connect-the-dots in a graph is a graph-theoretical problem with application to
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with application to the design of RFID-enabled surface for robot-assisted navigation.
Here a Review of the Combination of Machine Learning models from Bayesian Averaging, Committees to Boosting... Specifically An statistical analysis of Boosting is done
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Argumentation Theory provides tools for both modelling and reasoning with controversial information and is a methodology that is often used as a way to give explanations to results provided using machine learning techniques. In this con- text, labelling-based semantics for Abstract Argumentation Frameworks (AFs) allow for establishing the acceptability of sets of arguments, dividing them into three partitions: accept- able, rejected and undecidable (instead of classical Dung two sets IN and OUT partitions). This kind of semantics have been studied only for classical AFs, whilst the more powerful weighted and preference-based framework has been not studied yet. In this paper, we define a novel labelling semantics for Weighted Argumentation Frameworks, extending and generalising the crisp one.
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There are various reasons why we would want to find the extreme (maximum and minimum values) of a function. Fermat's Theorem tells us we can find local extreme points by looking at critical points. This process is known as the Closed Interval Method.
Uncountably many problems in life and nature can be expressed in terms of an optimization principle. We look at the process and find a few good examples.
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The aim of the study is to understand the selection process, that modulates the exploration mechanism, during the execution of a high cognitively demanding task. The main purpose is to identify the mechanism competition mechanism between top-down and bottom-up. We developed an adaptive system trying to emulate this mechanism.
In this article, first we generalize a few notions like (α ) - soft compatible maps, (β)- soft ompatible maps,soft compatible of type ( I ) and soft compatible of type ( II ) maps in oft metric spaces and then we give an accounts for comparison of these soft compatible aps. Finally, we demonstrate the utility of these new concepts by proving common fixed point theorem for fore soft continuous self maps on a complete soft metric space.
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A Matrix Based Approach for Weighted Argumentation FrameworksCarlo Taticchi
The assignment of weights to attacks in a classical Argumentation Framework allows to compute semantics by taking into account the different importance of each argument. We represent a Weighted Argumentation Framework by a non-binary matrix, and we characterise the basic extensions (such as w-admissible, w-stable, w-complete) by analysing sub-blocks of this matrix. Also, we show how to reduce the matrix into another one of smaller size, that is equivalent to the original one for the determination of extensions. Furthermore, we provide two algorithms that allow to build incrementally w-grounded and w-preferred extensions starting from a w-admissible extension.
論文紹介:
Pan, Wei-Xing, et al. "Dopamine cells respond to predicted events during classical conditioning: evidence for eligibility traces in the reward-learning network." The Journal of neuroscience 25.26 (2005): 6235-6242.
Connect-the-Dots in a Graph and Buffon's Needle on a Chessboard: Two Problems...Vladimir Kulyukin
We study two theoretical problems that arise naturally in the application domain of assisted
navigation. Connect-the-dots in a graph is a graph-theoretical problem with application to
robot indoor localization. Buffon’s needle on a chessboard is a problem in geometric probability
with application to the design of RFID-enabled surface for robot-assisted navigation.
Here a Review of the Combination of Machine Learning models from Bayesian Averaging, Committees to Boosting... Specifically An statistical analysis of Boosting is done
Extending Labelling Semantics to Weighted Argumentation FrameworksCarlo Taticchi
Argumentation Theory provides tools for both modelling and reasoning with controversial information and is a methodology that is often used as a way to give explanations to results provided using machine learning techniques. In this con- text, labelling-based semantics for Abstract Argumentation Frameworks (AFs) allow for establishing the acceptability of sets of arguments, dividing them into three partitions: accept- able, rejected and undecidable (instead of classical Dung two sets IN and OUT partitions). This kind of semantics have been studied only for classical AFs, whilst the more powerful weighted and preference-based framework has been not studied yet. In this paper, we define a novel labelling semantics for Weighted Argumentation Frameworks, extending and generalising the crisp one.
Lesson 18: Maximum and Minimum Values (Section 021 handout)Matthew Leingang
There are various reasons why we would want to find the extreme (maximum and minimum values) of a function. Fermat's Theorem tells us we can find local extreme points by looking at critical points. This process is known as the Closed Interval Method.
Uncountably many problems in life and nature can be expressed in terms of an optimization principle. We look at the process and find a few good examples.
Raw 2009 -THE ROLE OF LATEST FIXATIONS ON ONGOING VISUAL SEARCH A MODEL TO E...Giacomo Veneri
The aim of the study is to understand the selection process, that modulates the exploration mechanism, during the execution of a high cognitively demanding task. The main purpose is to identify the mechanism competition mechanism between top-down and bottom-up. We developed an adaptive system trying to emulate this mechanism.
In this article, first we generalize a few notions like (α ) - soft compatible maps, (β)- soft ompatible maps,soft compatible of type ( I ) and soft compatible of type ( II ) maps in oft metric spaces and then we give an accounts for comparison of these soft compatible aps. Finally, we demonstrate the utility of these new concepts by proving common fixed point theorem for fore soft continuous self maps on a complete soft metric space.
Solution to Black-Scholes P.D.E. via Finite Difference Methods (MatLab)Fynn McKay
Simple implementable of Numerical Analysis to solve the famous Black-Scholes P.D.E. via Finite Difference Methods for the fair price of a European option.
Characterizing the Distortion of Some Simple Euclidean EmbeddingsDon Sheehy
This talk addresses some upper and lower bounds techniques for bounding the distortion between mappings between Euclidean metric spaces including circles, spheres, pairs of lines, triples of planes, and the union of a hyperplane and a point.
A Matrix Based Approach for Weighted Argumentation FrameworksCarlo Taticchi
The assignment of weights to attacks in a classical Argumentation Framework allows to compute semantics by taking into account the different importance of each argument. We represent a Weighted Argumentation Framework by a non-binary matrix, and we characterise the basic extensions (such as w-admissible, w-stable, w-complete) by analysing sub-blocks of this matrix. Also, we show how to reduce the matrix into another one of smaller size, that is equivalent to the original one for the determination of extensions. Furthermore, we provide two algorithms that allow to build incrementally w-grounded and w-preferred extensions starting from a w-admissible extension.
論文紹介:
Pan, Wei-Xing, et al. "Dopamine cells respond to predicted events during classical conditioning: evidence for eligibility traces in the reward-learning network." The Journal of neuroscience 25.26 (2005): 6235-6242.
Li, Mu, et al. "Efficient mini-batch training for stochastic optimization." Proceedings of the 20th ACM SIGKDD international conference on Knowledge discovery and data mining. ACM, 2014.
http://www.cs.cmu.edu/~muli/file/minibatch_sgd.pdf
KDD2014勉強会関西会場: http://www.ml.ist.i.kyoto-u.ac.jp/kdd2014reading
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Optimal Asset Allocation using Adaptive Dynamic Programming
Neuneier. Ralph, In Advances in Neural Information Processing Systems. 1996.
Enhancing Q-Learning for Optimal Asset Allocation
Neuneier. Ralph, In Advances in Neural Information Processing Systems. 1998.
Master Thesis on the Mathematial Analysis of Neural NetworksAlina Leidinger
Master Thesis submitted on June 15, 2019 at TUM's chair of Applied Numerical Analysis (M15) at the Mathematics Department.The project was supervised by Prof. Dr. Massimo Fornasier. The thesis took a detailed look at the existing mathematical analysis of neural networks focusing on 3 key aspects: Modern and classical results in approximation theory, robustness and Scattering Networks introduced by Mallat, as well as unique identification of neural network weights. See also the one page summary available on Slideshare.
A pre conference workshop on Machine Learning was organized as a part of #doppa17, DevOps++ Global Summit 2017. The workshop was conducted by Dr. Vivek Vijay and Dr. Sandeep Yadav. All the copyrights are reserved with the author.
NP completeness. Classes P and NP are two frequently studied classes of problems in computer science. Class P is the set of all problems that can be solved by a deterministic Turing machine in polynomial time.
Slides were formed by referring to the text Machine Learning by Tom M Mitchelle (Mc Graw Hill, Indian Edition) and by referring to Video tutorials on NPTEL
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Whilst competitive headwinds remain, represented through the recent second bankruptcy filing of Sungard, which blames “COVID-19 and other macroeconomic trends including delayed customer spending decisions, insourcing and reductions in IT spending, energy inflation and reduction in demand for certain services”, the industry has seen key adjustments, where MCG believes that engineering cost management and technological innovation will be paramount to success.
MCG reports that the more favorable market conditions expected over the next few years, helped by the winding down of pandemic restrictions and a hybrid working environment will be driving market momentum forward. The continuous injection of capital by alternative investment firms, as well as the growing infrastructural investment from cloud service providers and social media companies, whose revenues are expected to grow over 3.6x larger by value in 2026, will likely help propel center provision and innovation. These factors paint a promising picture for the industry players that offset rising input costs and adapt to new technologies.
According to M Capital Group: “Specifically, the long-term cost-saving opportunities available from the rise of remote managing will likely aid value growth for the industry. Through margin optimization and further availability of capital for reinvestment, strong players will maintain their competitive foothold, while weaker players exit the market to balance supply and demand.”
Techniques to optimize the pagerank algorithm usually fall in two categories. One is to try reducing the work per iteration, and the other is to try reducing the number of iterations. These goals are often at odds with one another. Skipping computation on vertices which have already converged has the potential to save iteration time. Skipping in-identical vertices, with the same in-links, helps reduce duplicate computations and thus could help reduce iteration time. Road networks often have chains which can be short-circuited before pagerank computation to improve performance. Final ranks of chain nodes can be easily calculated. This could reduce both the iteration time, and the number of iterations. If a graph has no dangling nodes, pagerank of each strongly connected component can be computed in topological order. This could help reduce the iteration time, no. of iterations, and also enable multi-iteration concurrency in pagerank computation. The combination of all of the above methods is the STICD algorithm. [sticd] For dynamic graphs, unchanged components whose ranks are unaffected can be skipped altogether.
Explore our comprehensive data analysis project presentation on predicting product ad campaign performance. Learn how data-driven insights can optimize your marketing strategies and enhance campaign effectiveness. Perfect for professionals and students looking to understand the power of data analysis in advertising. for more details visit: https://bostoninstituteofanalytics.org/data-science-and-artificial-intelligence/
1. Principal Sensitivity Analysis
Sotetsu Koyamada (Presenter), Masanori Koyama, Ken Nakae, Shin Ishii
Graduate School of Informatics, Kyoto University
@PAKDD2015
May 20, 2015
Ho Chi Minh City, Viet Nam
3. Prediction and Recognition tasks at high accuracy
Machine learning is awesome
Horikawa et al., 2014
Taigman et al., 2014
Machines can carry out the tasks beyond human capability
Deep Learning matches human in the accuracy of face
Recognition tasks
Predicting the dream contents from Brain activities You can’t do
this unless you are Psychic!
4. How can the machines carry out the tasks beyond our capability?
How can we learn the machine’s
“secret” knowledge?
In the process of training, machines must have
learned the knowledge not in our natural scope
5. Machine is a black box
Neural Networks, Nonlinear kernel SVM, …
Input Classification
result
?
6. Visualizing the knowledge of Linear Model
The knowledge of the linear classifiers like Logistic Regression are
expressible in terms of weight parameters w = (w1,…, wd)
Classifier
Input x = (x1,…, xd)
Classification labels: {0, 1}
wi : weight parameter b: bias parameter
σ : sigmoid activation function
Meaning of wi = Importance of i-th input dimension
within machine’s knowledge
7. It is extremely difficult to make sense out of weight parameters in
Neural Networks (nonlinear composition of logistic regressions)
Visualizing the knowledge of non Linear Model
Our proposal
We shall directly analyze the behavior of f in the input space!
Meaning of wij
(k) = ???????
h: nonlinear activation function
9. Sensitivity analysis
Sensitivity analysis compute the sensitivity of f with respect to i-th input dimension
Def. Sensitivity with respect to i-th input dimension
Note
Def. Sensitivity map
Zurada et al., 1994, 97, Kjems et al., 2002
q: true distribution of x
In the case of linear model (e.g. logistic regression)
10. c.f. Sensitivity with respect to i-th input dimension
PSM: Principal Sensitivity Map
Define the directional sensitivity in the arbitrary direction
and seek the the direction to which the machine is most sensitive
Def. (1st) Principal Sensitivity Map
Def. Directional sensitivity in the direction v
Recall
ei: standard basis of
11. PSA: Principal Sensitivity Analysis
Define the kernel metric K as:
Def. (1st) Principal Sensitivity Map (PSM)
1st PSM is the dominant eigen vector of K!
When K is covariance matrix,
1st PSM is same as the 1st PC
Recall PSA vs PCA
12. PSA: Principal Sensitivity Analysis
Define the kernel metric K as:
Def. (1st) Principal Sensitivity Map (PSM)
1st PSM is the dominant eigen vector of K!
k-th PSM is the k-th dominant eigen vector of K!
Def. (k-th) Principal Sensitivity Map (PSM)
When K is covariance matrix,
1st PSM is same as the 1st PC
Recall
k-th PSM := analogue of k-th PC
PSA vs PCA
14. Digit classification
! Artificial Data Each pixel have the same meaning
! Classifier
– Neural Network (one hidden layer)
– Error percentage: 0.36%
– We applied the PSA to the log of each output from NN
(b) Noisy samples
(a) Templates
c = 0, …, 9
c = 0, ….9
15. Strength of PSA (relatively signed map)
(b) 1st PSMs (proposed)
(a) (Conventional) sensitivity maps
16. visualize the
values of
Strength of PSA (relatively signed map)
(Conventional) sensitivity map cannot distinguish
the set of the edges whose presence characterizes the class 1
and
The set of the edges whose absence characterizes the class 1
On the other hand, 1st PSM (proposed) can!
(b) 1st PSMs (proposed)
(a) (Conventional) sensitivity maps
visualize the
values of
17. Strength of the PSA (sub PSM)
PSMs of f9 (c = 9)
What is the meaning of sub PSMs
(Same as the previous slide)
18. Strength of the PSA (sub PSM)
PSMs (c = 9)
By definition, globally
important knowledge
Perhaps locally
important knowledge?
20. Local Sensitivity
Measure of the contribution of k-th PSM in the classification of class c
in the subset A
Def. Local sensitivity in the region A
sk
A := sA(vk)
k-th PSM
sA(v) := EA
∂fc(x)
∂v
2
Def. Local sensitivity in the direction of k-th PSM
21. Local Sensitivity
Measure of the contribution of k-th PSM in the classification of class c
in the subset A
Def. Local sensitivity in the region A
c = 9, k = 1, A = A(9,4) := set of all the samples of the classes 9 and 4
SA
k is The contribution of 1st PSM in the classification of 9 in the data
containing class 9 and 4
= The contribution of 1st PSM in distinguishing 9 from 4.
sk
A := sA(vk)
k-th PSM
sA(v) := EA
∂fc(x)
∂v
2
Def. Local sensitivity in the direction of k-th PSM
Example
22. Strength of the PSA (sub PSM)
Let’s look at what the knowledge of f9 is doing in distinguishing the
pairs of classes (class 9 vs the other class)
Local sensitivity of k-th PSM of f9 on the subdata
containing class 9 and class c’ ( = A(9, c’) )
c = 9
23. Strength of the PSA (sub PSM)
Let’s look at what the knowledge of f9 is doing in distinguishing the
pairs of classes (class 9 vs the other class)
Local sensitivity of k-th PSM of f9 on the subdata
containing class 9 and class c’
c = 9
Example: c = 9, c’ = 4, k = 1
Recall
This indicates the contribution of
1st PSM in distinguishing 9 from 4
24. Strength of the PSA (sub PSM)
Let’s look at what the knowledge of f9 is doing in distinguishing the
pairs of classes (class 9 vs the other class
Local sensitivity of k-th PSM of f9 on the subdata
containing class 9 and class C’ 3rd PSM contributes MUCH
more than the 1st PSM in the
classification of 9 against 4!!!c = 9
25. In fact….!
PSM
(c = 9, k = 3)
We can visually confirm that the 3rd PSM of f9 is indeed the knowledge
of the machine that helps (MUCH!) in distinguishing 9 from 4!
94
26. When PSMs are difficult to interpret
• PSMs of NN trained from MNIST data in classifying 10 digits
• Each pixel have different meaning
• In order to applying PSA, Data should be registered
28. Conclusion
Can identify the sets of input dimensions that acts
oppositely in characterizing the classes
Sub PSMs provide additional information of the machines
(possibly local)
PSA is different from the original sensitivity analysis in that it identifies
the weighted combination of the input dimensions that are essential in
the machine’s knowledge
2
1
Made possible with the definition of the PSMs that allows
negative elements
Merits of PSA
Sotetsu Koyamada
koyamada-s@sys.i.kyoto-u.ac.jpThank you