Machine Learning Challenges in Astronomy
-
Upload
cosmoaims-bassett -
Category
Technology
-
view
520 -
download
2
description
Transcript of Machine Learning Challenges in Astronomy
![Page 1: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/1.jpg)
![Page 2: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/2.jpg)
Ninan Sajeeth PhilipNinan Sajeeth Philip
St. Thomas College, Kozhencherry
![Page 3: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/3.jpg)
Ninan Sajeeth PhilipNinan Sajeeth Philip
St. Thomas College, Kozhencherry
![Page 4: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/4.jpg)
I am visiting Sudhanshu Barway as part of the joint SouthAfrica India bilateral project with SAAO for developing Virtual Observatory tools for SALT.
![Page 5: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/5.jpg)
Machine Learning Challenges in Astronomy
Ninan Sajeeth [email protected]
http://www.iucaa.ernet.in/~nspp
![Page 6: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/6.jpg)
Machine Learning
● Objective : Mimic human ability to learn and make decisions.
● Need : Surveys are producing huge data and conventional methods are insufficient to process them. Eg: SDSS survey could spectroscopically confirm the nature of only less than 1% of its photometric detections.
● Limitation : The goodness of the outputs depend on the discriminative power of the inputs.
● Advantage : First level sorting of candidates.
![Page 7: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/7.jpg)
Machine Learning
● Objective : Mimic human ability to learn and make decisions.
● Need : Surveys are producing huge data and conventional methods are insufficient to process them. Eg: SDSS survey could spectroscopically confirm the nature of only less than 1% of its photometric detections.
● Limitation : The goodness of the outputs depend on the discriminative power of the inputs.
● Advantage : First level sorting of candidates.
![Page 8: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/8.jpg)
Machine Learning
● Objective : Mimic human ability to learn and make decisions.
● Need : Surveys are producing huge data and conventional methods are insufficient to process them. Eg: SDSS survey could spectroscopically confirm the nature of only less than 1% of its photometric detections.
● Limitation : The goodness of the outputs depend on the discriminative power of the inputs.
● Advantage : First level sorting of candidates.
![Page 9: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/9.jpg)
Machine Learning
● Objective : Mimic human ability to learn and make decisions.
● Need : Surveys are producing huge data and conventional methods are insufficient to process them. Eg: SDSS survey could spectroscopically confirm the nature of only less than 1% of its photometric detections.
● Limitation : The goodness of the outputs depend on the discriminative power of the inputs.
● Advantage : First level sorting of candidates.
![Page 10: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/10.jpg)
Machine Learning
● Objective : Mimic human ability to learn and make decisions.
● Need : Surveys are producing huge data and conventional methods are insufficient to process them. Eg: SDSS survey could spectroscopically confirm the nature of only less than 1% of its photometric detections.
● Limitation : The goodness of the outputs depend on the discriminative power of the inputs.
● Advantage : First level sorting of candidates.
![Page 11: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/11.jpg)
Large Data Issues
● Multidimensional data – requires more memory● Diversity in the data – rare to rich populations● Overlapping features – observational limitations● Missing values – observational limitations● Uncertainties – inherent and observational● Processing Power – silicon limitations● Storage and retrieval – bandwidth limitations
![Page 12: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/12.jpg)
Large Data Issues
● Multidimensional data – requires more memory● Diversity in the data – rare to rich populations● Overlapping features – observational limitations● Missing values – observational limitations● Uncertainties – inherent and observational● Processing Power – silicon limitations● Storage and retrieval – bandwidth limitations
![Page 13: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/13.jpg)
Large Data Issues
● Multidimensional data – requires more memory● Diversity in the data – rare to rich populations● Overlapping features – observational limitations● Missing values – observational limitations● Uncertainties – inherent and observational● Processing Power – silicon limitations● Storage and retrieval – bandwidth limitations
![Page 14: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/14.jpg)
Large Data Issues
● Multidimensional data – requires more memory● Diversity in the data – rare to rich populations● Overlapping features – observational limitations● Missing values – observational limitations● Uncertainties – inherent and observational● Processing Power – silicon limitations● Storage and retrieval – bandwidth limitations
![Page 15: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/15.jpg)
Large Data Issues
● Multidimensional data – requires more memory● Diversity in the data – rare to rich populations● Overlapping features – observational limitations● Missing values – observational limitations● Uncertainties – inherent and observational● Processing Power – silicon limitations● Storage and retrieval – bandwidth limitations
![Page 16: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/16.jpg)
Large Data Issues
● Multidimensional data – requires more memory● Diversity in the data – rare to rich populations● Overlapping features – observational limitations● Missing values – observational limitations● Uncertainties – inherent and observational● Processing Power – silicon limitations● Storage and retrieval – bandwidth limitations
![Page 17: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/17.jpg)
Large Data Issues
● Multidimensional data – requires more memory● Diversity in the data – rare to rich populations● Overlapping features – observational limitations● Missing values – observational limitations● Uncertainties – inherent and observational● Processing Power – silicon limitations● Storage and retrieval – bandwidth limitations
![Page 18: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/18.jpg)
Different Machine Learning Methods● All methods assume that the different types
(classes) are separable in the feature space.
Light profile of galaxies are different from that of stars
![Page 19: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/19.jpg)
A Real Example
Composed of about a million points showing clustering of Quasars (blue and red), main sequence stars (green), late type stars (yellow) and unresolved galaxies (pink) in a colour colour plot of SDSS colours.
SDSS colourcolour plot
![Page 20: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/20.jpg)
A Real Example
Composed of about a million points showing clustering of Quasars (blue and red), main sequence stars (green), late type stars (yellow) and unresolved galaxies (pink) in a colour colour plot of SDSS colours.
Blue are low redshift Quasars and our goal is to identify them and verify whether the actual number count match with the estimated values.
![Page 21: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/21.jpg)
A Real Example Blue are low redshift Quasars and our goal is to identify them and verify whether the actual number count match with the estimated values.
The region in the box has about 150,000 confirmed observations and about 6 million unconfirmed cases.
![Page 22: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/22.jpg)
A Real Example Blue are low redshift Quasars and our goal is to identify them and verify whether the actual number count match with the estimated values.
The region in the box has about 150,000 confirmed observations and about 6 million unconfirmed cases.
All objects have known colours – only their classification is unknown.
![Page 23: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/23.jpg)
Bayesian Model
![Page 24: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/24.jpg)
Feature Space
● SDSS provides 5 magnitudes for each object in bands u, g, r, i and z that can be used to construct a ten dimensional colour space.
● A subset of the 150,000 objects with confirmed spectroscopic classification can be used to estimate the likelihood.
● The classifier can be tested on remaining data to verify the accuracy of the model.
![Page 25: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/25.jpg)
Feature Space
● SDSS provides 5 magnitudes for each object in bands u, g, r, i and z that can be used to construct a ten dimensional colour space.
● A subset of the 150,000 objects with confirmed spectroscopic classification can be used to estimate the likelihood.
● The classifier can be tested on remaining data to verify the accuracy of the model.
The distribution is not smooth
![Page 26: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/26.jpg)
Feature Space● SDSS provides 5 magnitudes for each object in
bands u, g, r, i and z that can be used to construct a ten dimensional colour space.
● A subset of the 150,000 objects with confirmed spectroscopic classification can be used to estimate the likelihood.
The colour space need to be binned to approximate the distribution.
● The classifier can be tested on remaining data to verify the accuracy of the model.
The distribution is not smooth
![Page 27: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/27.jpg)
Feature Space● SDSS provides 5 magnitudes for each object in bands u,
g, r, i and z that can be used to construct a ten dimensional colour space.
● A subset of the 150,000 objects with confirmed spectroscopic classification can be used to estimate the likelihood.
The colour space need to be binned to approximate the distribution. Computing conditional likelihood of the binned high dimensional feature space is nearly impossible.
● The classifier can be tested on remaining data to verify the accuracy of the model.
The distribution is not smooth
![Page 28: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/28.jpg)
Two issues with Bayesian Formalism
● How would you guess the True value of the Prior for each bin?
● Conditional dependency of the input feature space – likelihood is conditionally dependent on input values Naive Bayesian models fail on even simple XOR problems.
![Page 29: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/29.jpg)
Bayesian Methods● Ensemble methods: Multiple models, same data : many
weak learners combined to form a strong learning model
● Bagging: each model in ensemble vote for the probable candidate
● Boosting: Emphasise the failing models with weights● Bayesian Model Averaging (BMA): Sampling
Hypothesis from Hypothesis Space● Bayesian Model Combination (BMC): Seek
combination of models closest to a distribution.
![Page 30: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/30.jpg)
Bayesian Methods● Ensemble methods: Multiple models, same data● Bagging: each model in ensemble vote for the
probable candidate● Boosting: Emphasise the failing models with
weights● Bayesian Model Averaging (BMA): Sampling
Hypothesis from Hypothesis Space● Bayesian Model Combination (BMC): Seek
combination of models closest to a distribution.
![Page 31: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/31.jpg)
Bayesian Methods● Ensemble methods: Multiple models, same data● Bagging: each model in ensemble vote for the
probable candidate● Boosting: Emphasise the failing models with
weights● Bayesian Model Averaging (BMA): Sampling
Hypothesis from Hypothesis Space● Bayesian Model Combination (BMC): Seek
combination of models closest to a distribution.
![Page 32: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/32.jpg)
Bayesian Methods● Ensemble methods: Multiple models, same data● Bagging: each model in ensemble vote for the
probable candidate● Boosting: Emphasise the failing models with
weights● Bayesian Model Averaging (BMA): Sampling
Hypothesis from Hypothesis Space● Bayesian Model Combination (BMC): Seek
combination of models closest to a distribution.
![Page 33: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/33.jpg)
Bayesian Methods● Ensemble methods: Multiple models, same data● Bagging: each model in ensemble vote for the
probable candidate● Boosting: Emphasise the failing models with
weights● Bayesian Model Averaging (BMA): Sampling
Hypothesis from Hypothesis Space● Bayesian Model Combination (BMC): Seek a
combination of models closest to a distribution.
![Page 34: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/34.jpg)
Our Solution
● Estimating both Prior and Likelihood from data.● Boosting: Emphasise the failing models with
weights
Can Prior be replaced with weights for each range (bin) of input feature values within the same model?
![Page 35: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/35.jpg)
Replacing Prior with weights● Partition the input feature space into M bins – the bins the bins
can be centred around clusters or simple uniform binning.can be centred around clusters or simple uniform binning.
● Assign uniform small prior/weight to all the bins.Assign uniform small prior/weight to all the bins.● Compute Bayesian Posterior Probability based on Compute Bayesian Posterior Probability based on
input features in the training data and identify failed input features in the training data and identify failed instances.instances.
● Update weights associated with the input feature Update weights associated with the input feature bins corresponding to failed cases by A bins corresponding to failed cases by A x x (1P/P*) (1P/P*) where A is a learning constant and P and P* are BP where A is a learning constant and P and P* are BP for failed and target outcomes respectively.for failed and target outcomes respectively.
![Page 36: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/36.jpg)
Replacing Prior with weights● Partition the input feature space into M bins – the bins the bins
can be centred around clusters or simple uniform binning.can be centred around clusters or simple uniform binning.
● Assign Assign uniformuniform small prior/weight to all the bins. small prior/weight to all the bins.● Compute Bayesian Posterior Probability based on Compute Bayesian Posterior Probability based on
input features in the training data and identify failed input features in the training data and identify failed instances.instances.
● Update weights associated with the input feature Update weights associated with the input feature bins corresponding to failed cases by A bins corresponding to failed cases by A x x (1P/P*) (1P/P*) where A is a learning constant and P and P* are BP where A is a learning constant and P and P* are BP for failed and target outcomes respectively.for failed and target outcomes respectively.
![Page 37: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/37.jpg)
Replacing Prior with weights● Partition the input feature space into M bins – the bins the bins
can be centred around clusters or simple uniform binning.can be centred around clusters or simple uniform binning.
● Assign Assign uniformuniform small prior/weight to all the bins. small prior/weight to all the bins.● Compute Bayesian Posterior Probability based on Compute Bayesian Posterior Probability based on
input features in the training data and input features in the training data and identify failed identify failed instances.instances.
● Update weights associated with the input feature Update weights associated with the input feature bins corresponding to failed cases by A bins corresponding to failed cases by A x x (1P/P*) (1P/P*) where A is a learning constant and P and P* are BP where A is a learning constant and P and P* are BP for failed and target outcomes respectively.for failed and target outcomes respectively.
![Page 38: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/38.jpg)
Replacing Prior with weights● Partition the input feature space into M bins – the bins the bins
can be centred around clusters or simple uniform binning.can be centred around clusters or simple uniform binning.
● Assign Assign uniformuniform small prior/weight to all the bins. small prior/weight to all the bins.● Compute Bayesian Posterior Probability based on Compute Bayesian Posterior Probability based on
input features in the training data and input features in the training data and identify failed identify failed instances.instances.
● Update weights associated with the input feature Update weights associated with the input feature bins corresponding to failed cases by bins corresponding to failed cases by A A x x (1P/P*)(1P/P*) where where AA is a learning constant and is a learning constant and PP and and P*P* are BP are BP for failed and target outcomes respectively.for failed and target outcomes respectively.
![Page 39: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/39.jpg)
Replacing Prior with weights● Partition the input feature space into M bins – the bins the bins
can be centred around clusters or simple uniform binning.can be centred around clusters or simple uniform binning.
● Assign Assign uniformuniform small prior/weight to all the bins. small prior/weight to all the bins.● Compute Bayesian Posterior Probability based on Compute Bayesian Posterior Probability based on
input features in the training data and input features in the training data and identify failed identify failed instances.instances.
● Update weights associated with the input feature Update weights associated with the input feature bins corresponding to failed cases by bins corresponding to failed cases by A A x x (1P/P*)(1P/P*) where A is a learning constant and P and P* are BP where A is a learning constant and P and P* are BP for failed and target outcomes respectively. for failed and target outcomes respectively. Since the Since the update is based on probability, outliers do not cause an issue.update is based on probability, outliers do not cause an issue.
![Page 40: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/40.jpg)
Likelihood estimation of Binned Space● Likelihood estimation becomes an issue because
we want to know the conditional likelihood of the binned feature space. There may not be sufficient samples in each bin to estimate likelihood when conditional dependence constrains are imposed on them.
● We adopted an imposed conditional independence formula that approximate the likelihood for a conditionally dependent event as the product of the likelihood for pairs of input features.
![Page 41: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/41.jpg)
Likelihood estimation of Binned Space● Likelihood estimation becomes an issue because
we want to know the conditional likelihood of the binned feature space. There may not be sufficient samples to estimate likelihood when constrains on conditional dependence is imposed on them.
● We adopted an imposed conditional independence formula that approximate the likelihood for a conditionally dependent event as the product of the likelihood for pairs of input features.
![Page 42: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/42.jpg)
Imposed Conditional Independence
The likelihood for a conditionally dependent event A can be approximated as the product of the likelihood of paired input features.
● L(A|b,c,d,e,f) ~
M*L(A|b,c)* L(A|b,d)* L(A|b,e)* L(A|b,f)* L(A|c,d) *L(A|c,e)* L(A|c,f)* L(A|d,e)* L(A|d,f)* L(A|e,f)
● Works better than Naive Bayes – no issue with XOR gate
![Page 43: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/43.jpg)
Imposed Conditional Independence
The likelihood for a conditionally dependent event A can be approximated as the product of the likelihood of its paired inputs.
● L(A|b,c,d,e,f) ~
M*L(A|b,c)* L(A|b,d)* L(A|b,e)* L(A|b,f)* L(A|c,d) *L(A|c,e)* L(A|c,f)* L(A|d,e)* L(A|d,f)* L(A|e,f)
● Works better than Naive Bayes – no issue with XOR gate
![Page 44: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/44.jpg)
Classification of the 6 million Objects
Blue are Quasars, Yellow are unresolved Galaxies and Green are main sequence Stars
![Page 45: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/45.jpg)
Verification of Predictions
![Page 46: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/46.jpg)
Comparison with expected number counts
![Page 47: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/47.jpg)
Further Information
![Page 48: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/48.jpg)
The Predicted Catalogue
![Page 49: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/49.jpg)
A more complex situation
● What if all input features are not known?
Straightforward solution : Compute the inverse probability for the missing feature just as you handle missing values.
Not so easy situation: What if we do not have a training data with all features for computing inverse probability?
![Page 50: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/50.jpg)
A more complex situation
● What if all input features are not known?
Straightforward solution : Compute the inverse probability for the missing feature just as you handle missing values.
Not so easy situation: What if we do not have a training data with all features for computing inverse probability?
![Page 51: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/51.jpg)
A more complex situation
● What if all input features are not known?
Straightforward solution : Compute the inverse probability for the missing feature just as you handle missing values.
Not so easy situation: What if we do not have a training data with all features for computing inverse probability?
![Page 52: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/52.jpg)
A Challenging Problem
![Page 53: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/53.jpg)
A Challenging Problem● Generate alerts on optical transient detections● Minimize false alarms● Customize alarms to user demands● Send the alarms immediately – given minimal or
sometime very little information about it.
Example : Nearest distance to a galaxy or star
: Distance to nearest known radio object : Distance to nearest known xray detections : Magnitudes in archives and in earlier detections
![Page 54: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/54.jpg)
A Challenging Problem
● Generate alerts on optical transient detections● Minimize false alarms● Customize alarms to user demands● Send the alarms immediately – given minimal or
sometime very little information about it.
Example : Nearest distance to a galaxy or star
: Distance to nearest known radio object : Distance to nearest known xray detections : Magnitudes in archives and in earlier detections
![Page 55: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/55.jpg)
A Challenging Problem
● Generate alerts on optical transient detections● Minimize false alarms● Customize alerts to user demands● Send the alarms immediately – given minimal
or sometime very little information about it.
Example : Nearest distance to a galaxy or star
: Distance to nearest known radio object : Distance to nearest known xray detections : Magnitudes in archives and in earlier detections
![Page 56: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/56.jpg)
A Challenging Problem● Generate alerts on optical transient detections● Minimize false alarms● Customize alarms to user demands● Send the alerts immediately – given minimal or
sometime very little information about it.
Example : Nearest distance to a galaxy or star
: Distance to nearest known radio object : Distance to nearest known xray detections : Magnitudes in archives and in earlier detections
![Page 57: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/57.jpg)
A Challenging Problem● Generate alerts on optical transient detections● Minimize false alarms● Customize alarms to user demands● Send the alerts immediately – given minimal or
sometime very little information about it.
Example : Nearest distance to a galaxy or star
: Distance to nearest known radio object : Distance to nearest known xray detections : Magnitudes in archives and in earlier detections
![Page 58: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/58.jpg)
Missing Values
Example : Nearest distance to a galaxy or star
: Distance to nearest known radio object : Distance to nearest known xray detections : Magnitudes in archives and in earlier detections
Possible only if the object is within the foot print of a survey
Each survey may use a different unit for their catalogues – need to be considered separately
![Page 59: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/59.jpg)
Missing Values
Example : Nearest distance to a galaxy or star
: Distance to nearest known radio object : Distance to nearest known xray detections : Magnitudes in archives and in earlier detections
Possible only if the object is within the foot print of a survey
Each survey may use a different unit for their catalogues – need to be considered separately
![Page 60: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/60.jpg)
Missing Data Values
The training data itself has missing data values.Note: The accuracy of the actual observation is not beyond one or two decimal places. The double precision is used here only to reduce round off error while rescaling the data during the processing.
![Page 61: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/61.jpg)
Missing Values
No way to compute inverse probability makes
No way to compute inverse probability makes
it impossible for standard machine learning
it impossible for standard machine learning
algorithms to learn and predict the outcome
algorithms to learn and predict the outcome
![Page 62: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/62.jpg)
Our Approach
The likelihood for a conditionally dependent event A can be approximated as the product of the likelihood of its paired inputs.
● L(A|b,c,d,e,f) ~
M*L(A|b,c)* L(A|b,d)* L(A|b,e)* L(A|b,f)* L(A|c,d) *L(A|c,e)* L(A|c,f)* L(A|d,e)* L(A|d,f)* L(A|e,f)
![Page 63: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/63.jpg)
Our Approach
The likelihood for a conditionally dependent event A can be approximated as the product of the likelihood of its paired inputs.
● L(A|b,c,d,e,f) ~
M*L(A|b,c)* L(A|b,d)* L(A|b,e)* L(A|b,f)* L(A|c,d) *L(A|c,e)* L(A|c,f)* L(A|d,e)* L(A|d,f)* L(A|e,f)
![Page 64: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/64.jpg)
Our Approach
The likelihood for a conditionally dependent event A can be approximated as the product of the likelihood of its paired inputs.
● L(A|b,c,d,e,f) ~
M*L(A|b,c)* L(A|b,d)* L(A|b,e)* L(A|b,f)* L(A|c,d) *L(A|c,e)* L(A|c,f)* L(A|d,e)* L(A|d,f)* L(A|e,f)
● Estimate approximate Likelihood based on whatever information available and use it for training and testing.
![Page 65: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/65.jpg)
Approximate Likelihood
● Since we do not have the luxury to decide the input features, we go for a greedy collection of what all information – input data – that can be collected to compute the approximate likelihood.
● It is expected (assumed) that the redundancy in the available information will help us to approximate the likelihood to some reasonable accuracy.
![Page 66: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/66.jpg)
Approximate Likelihood
● Since we do not have the luxury to decide the input features, we go for a greedy collection of what all information – input data – that can be collected to compute the approximate likelihood.
● It is expected (assumed) that the redundancy in the available information will help us to approximate the likelihood to some reasonable accuracy.
![Page 67: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/67.jpg)
Approximate Likelihood
● Since we do not have the luxury to decide the input features, we go for a greedy collection of what all information – input data – that can be collected to compute the approximate likelihood.
● It is expected (assumed) that the redundancy in the available information will help us to approximate the likelihood to some reasonable accuracy.
More like a forensic investigationMore like a forensic investigation
![Page 68: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/68.jpg)
What about Prior?
The likelihood for a conditionally dependent event A is approximated to the product of the likelihood of paired input features.
The prior is to be determined from the data
Uses a gradient descent algorithm to determine the prior from the data
![Page 69: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/69.jpg)
What about Prior?
The likelihood for a conditionally dependent event A can is approximated to the product of the likelihood of paired input features.
The prior is to be determined from the data with missing data
We use a gradient descent algorithm to determine the prior from the data
![Page 70: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/70.jpg)
What about Prior?
The likelihood for a conditionally dependent event A is approximated as the product of the likelihood of paired input features.
The prior is to be determined from the data with missing data
We use a gradient descent algorithm to determine the prior – weights from the data, similar to boosting.
![Page 71: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/71.jpg)
Dynamic Learning
● With lot of missing values in the observations, each input data has partial information about the features associated to an outcome.
● Learn as we go... use Bayesian update rule to update the belief in each input feature and its consequences.
![Page 72: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/72.jpg)
Dynamic Learning
● With lot of missing values in the observations, each input data has partial information about the features associated to an outcome.
● Learn as we go... use Bayesian update rule to update the belief in each input feature and its effect on the outcome.
![Page 73: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/73.jpg)
Dynamic Addition of Features
● We want to use all available information about the detections as and when they become available.
● Since likelihood is computed as the product, it is feasible to update it with new evidences as and when they become available.
![Page 74: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/74.jpg)
Dynamic Addition of Features
● We want to use all available information about the detections
● Since likelihood is computed as the product, it is feasible to update it with new evidences as and when they become available.
![Page 75: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/75.jpg)
Dreaming Computers
● We now have many input features but not so many examples to learn from. This can lead to overfitting the data and Memorising rather than generalising the situation.
● Dreams are synthetic inputs our brain uses to teach us how to react to plausible situations. Can we create dreams for computers?
![Page 76: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/76.jpg)
Dreaming Computers
● We now have many input features but not so many examples to learn from. This can lead to overfitting the data and Memorising rather than generalising the situation.
● Dreams are synthetic inputs our brain uses to teach us how to react to plausible situations. Can we create dreams for computers?
![Page 77: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/77.jpg)
Information from Error Bars
● Can error bars give additional information?
● Error bars tell us that the nature of the object remains same even if the measurement value is varied within the range of the error bar – can be used to generate new data
![Page 78: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/78.jpg)
Information from Error Bars
● Can error bars give additional information?
● Error bars tell us that the nature of the object remains same even if the measurement value is varied within the range of the error bar – can be used to generate new data
![Page 79: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/79.jpg)
DBNN
● The algorithm described so far is the core design concept of the Difference Boosting Neural Network or DBNN algorithm.
● It is GNU public and the source code can be downloaded from
http://www.iucaa.ernet.in/~nspp/dbnn.html
![Page 80: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/80.jpg)
DBNN Annotator
A collaborative project with Ashish Mahabal A collaborative project with Ashish Mahabal (Caltech), IUCAA, Pune and the CRTS Team (Caltech), IUCAA, Pune and the CRTS Team with funding from IUSSTF and ISRO.with funding from IUSSTF and ISRO.
![Page 81: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/81.jpg)
CRTS Predictions
1, "Cataclysmic Variable"2 "Supernova"3 "other"5 "Blazar Outburst"6 "AGN Variability"7 "UVCeti Variable"8 "Asteroid"9 "Variable"10 "Mira Variable"11 "High Proper Motion Star"12 "Comet"
![Page 82: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/82.jpg)
CRTS Predictions
[1] [2] [3] [5] [6] [7] [8] [9] [10] [11] [12] [16] Total [1] 273 3 4 1 1 0 1 3 3 3 0 1 293 [2] 4 402 3 0 4 1 3 2 0 1 1 0 421 [3] 0 0 34 0 0 0 0 0 0 0 0 0 34 [5] 0 0 0 60 0 0 0 0 1 0 0 0 61 [6] 0 0 0 0 126 0 0 0 0 0 0 0 126 [7] 0 0 0 0 0 32 0 0 0 0 0 0 32 [8] 0 0 0 0 0 0 6 0 0 0 0 0 6 [9] 0 0 0 0 0 0 0 18 0 0 0 0 18 [10] 0 0 0 0 0 0 0 0 12 0 0 0 12 [11] 0 0 0 0 0 0 0 0 0 43 0 0 43 [12] 0 0 0 0 0 0 0 0 0 0 5 0 5 [16] 0 0 0 0 0 0 0 0 0 0 0 1 1 _________________________________________________________Total 277 405 41 61 131 33 10 23 16 47 6 2 1052
1,"Cataclysmic Variable"2,"Supernova"3,"other"5,"Blazar Outburst"6,"AGN Variability"7,"UVCeti Variable"8,"Asteroid"9,"Variable"10,"Mira Variable"11,"High Proper Motion Star"12,"Comet"
![Page 83: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/83.jpg)
CRTS Predictions
[1] [2] [3] [5] [6] [7] [8] [9] [10] [11] [12] [16] Total [1] 273 3 4 1 1 0 1 3 3 3 0 1 293 [2] 4 402 3 0 4 1 3 2 0 1 1 0 421 [3] 0 0 34 0 0 0 0 0 0 0 0 0 34 [5] 0 0 0 60 0 0 0 0 1 0 0 0 61 [6] 0 0 0 0 126 0 0 0 0 0 0 0 126 [7] 0 0 0 0 0 32 0 0 0 0 0 0 32 [8] 0 0 0 0 0 0 6 0 0 0 0 0 6 [9] 0 0 0 0 0 0 0 18 0 0 0 0 18 [10] 0 0 0 0 0 0 0 0 12 0 0 0 12 [11] 0 0 0 0 0 0 0 0 0 43 0 0 43 [12] 0 0 0 0 0 0 0 0 0 0 5 0 5 [16] 0 0 0 0 0 0 0 0 0 0 0 1 1 _________________________________________________________Total 277 405 41 61 131 33 10 23 16 47 6 2 1052
1,"Cataclysmic Variable"2,"Supernova"3,"other"5,"Blazar Outburst"6,"AGN Variability"7,"UVCeti Variable"8,"Asteroid"9,"Variable"10,"Mira Variable"11,"High Proper Motion Star"12,"Comet"
Recall 273/277 =98.5%→False Alarms (293273)/293 = 7%→
![Page 84: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/84.jpg)
Parallel DBNN
● Since DBNN split likelihood as the product of individual pairs, computation of likelihood may be independently carried out by a different node in a HPC system.
● Broadcast likelihoods to nodes● Compute● Gather Bayesian belief for each outcome
![Page 85: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/85.jpg)
Parallel DBNN
● Since DBNN split likelihood as the product of individual pairs, computation of likelihood may be independently carried out by a different node in a HPC system.
● Broadcast likelihoods to nodes● Compute● Gather Bayesian belief for each outcome
![Page 86: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/86.jpg)
Parallel DBNN
● Since DBNN split likelihood as the product of individual pairs, computation of likelihood may be independently carried out by a different node in a HPC system.
● Broadcast likelihoods to nodes● Compute● Gather Bayesian belief for each outcome
![Page 87: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/87.jpg)
Parallel DBNN
● Since DBNN split likelihood as the product of individual pairs, computation of likelihood may be independently carried out by a different node in a HPC system.
● Broadcast likelihoods to nodes● Compute● Gather Bayesian belief for each outcome
![Page 88: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/88.jpg)
Parallel DBNN Code
Ajay Vibhute
Photometric Redshift Estimation
8 million Point sources from SDSSRedshift with a step size of 0.05Ranging from 0 to 7
Four compute nodes, 16 Gb RAMTraining time reduced from 3 days to 11 hours
![Page 89: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/89.jpg)
Parallel DBNN Code
Ajay Vibhute
Photometric Redshift Estimation
8 million Point sources from SDSSRedshift with a step size of 0.05Ranging from 0 to 7
Four compute nodes, 16 Gb RAMTraining time reduced from 3 days to 11 hours
![Page 90: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/90.jpg)
Parallel DBNN Code
Ajay Vibhute
Photometric Redshift Estimation
8 million Point sources from SDSSRedshift with a step size of 0.05Ranging from 0 to 7
Four compute nodes, 16 Gb RAMTraining time reduced from 3 days to 11 hours
![Page 91: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/91.jpg)
Parallel DBNN Code
Ajay Vibhute
Photometric Redshift Estimation
8 million Point sources from SDSSRedshift with a step size of 0.05Ranging from 0 to 7
Four compute nodes, 16 Gb RAMTraining time reduced from 3 days to 11 hours
![Page 92: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/92.jpg)
Parallel DBNN ResultsPhotometric redshift estimation of unresolved SDSS detections compared with spectroscopically confirmed samples.
Unpublished : under preparation
![Page 93: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/93.jpg)
Parallel DBNN Results
![Page 94: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/94.jpg)
Work in Progress
● Use of features extracted from light curves can improve the classification
● Not all interesting objects – discoveries – may have light curves
● A VO Machine learning Tool kit is under development
● It will provide a VO compatible platform for astronomical data mining.
![Page 95: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/95.jpg)
Work in Progress● Use of features extracted from light curves can
improve the classification
Eclipsing Binary
Planetary System
Red Giant
![Page 96: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/96.jpg)
Work in Progress
● Use of features extracted from light curves can improve the classification
Correlation analysis of 58 features extracted from CRTS light curves.
Arun Kumar
![Page 97: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/97.jpg)
Work in Progress
● Use of features extracted from light curves can improve the classification
● Not all interesting objects – discoveries – may have light curves
● A VO Machine learning Tool kit is under development
● It will provide a VO compatible platform for astronomical data mining.
![Page 98: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/98.jpg)
Work in Progress● Use of features extracted from light curves can
improve the classification
Spectroscopic Pipeline for the Double Spectrograph at Palomar Observatory
Sheelu Abraham
![Page 99: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/99.jpg)
Work in Progress
● Use of features extracted from light curves can improve the classification
● Not all interesting objects – discoveries – may have light curves
● A VO Machine learning Tool kit is under development
● It will provide a VO compatible platform for astronomical data mining.
![Page 100: Machine Learning Challenges in Astronomy](https://reader034.fdocuments.us/reader034/viewer/2022052618/554abed0b4c905ec6c8b4a9a/html5/thumbnails/100.jpg)
Photometric Databases and Data Analysis Techniques
Indo US Joint Centers
Jan 2024th 2014
1. CLASS ACT IUCAA, Caltech, St. Thomas College
2. Variable Stars Univ. Delhi, SUNY Oswego, Univ. of Florida, Gainesville, Texas A&M Univ., IUCAAA