ActivePrediction

[Experimental]

ActivePrediction[f,{conf₁,conf₂, …}]

gives an object representing the result of active prediction obtained by using the function f to determine values for the example configurations conf_i.

ActivePrediction[f,reg]

generates configurations within the region specified by reg.

ActivePrediction[f,sampler]

generates configurations by applying the function sampler.

ActivePrediction[f,{conf₁,conf₂,…}nsampler]

applies the function nsampler to successively generate configurations starting from one of the conf_i.

Details and Options

ActivePrediction[…] returns an ActivePredictionObject[…] whose properties can be obtained using ActivePredictionObject[…]["prop"].
Possible properties include:

	"EvaluationHistory"	configurations explored and values corresponding to them
	"Method"	method used for active prediction
	"PredictorFunction"	best PredictorFunction[…] obtained
	"PredictorMeasurementsObject"	latest PredictorMeasurementsObject[…] obtained
	"OracleFunction"	original function f used to determine values
	"LearningCurve"	plot of mean cross-entropy evolution
	"Properties"	list of all available properties

Configurations can be of any form accepted by Predict (single data element, list of data elements, association of data elements, etc.) and of any type accepted by Predict (numerical, textual, sounds, images, etc.).
When applied to a configuration conf, the output of the function f must be a real-number value.
In ActivePrediction[f,spec], spec defines the domain of the function f. A domain can be defined by a list of configurations, a geometric region or a configuration generator function.
In ActivePrediction[f,sampler], sampler[] must output a configuration suitable for f to be applied to it.
In ActivePrediction[f,{conf₁,conf₂,…}nsampler], nsampler[conf] must output a configuration.
ActivePrediction has the same options as Predict, with the following additions and changes: [List of all options]

InitialEvaluationHistory	None	initial set of configurations and values
MaxIterations	2000	maximum number of iterations
Method	Automatic	method used to determine configurations to query and the prediction algorithm to use
RandomSeeding	1234	what seeding of pseudorandom generators should be done internally

Possible settings for Method include:

	Automatic	automatically choose method
	"Randomized"	choose random configurations from the domain
	"MaxEntropy"	choose configurations for which the predictor has maximum uncertainty
	assoc	association specifying the evaluation strategy and prediction method

In the form Methodassoc, the association can have elements:
"EvaluationStrategy" method for determining which configurations to query

"PredictionMethod" method to use for prediction
Possible settings for RandomSeeding include:

	Automatic	automatically reseed every time the function is called
	Inherited	use externally seeded random numbers
	seed	use an explicit integer or strings as a seed

List of all options

AcceptanceThreshold	Automatic	rarer probability threshold for anomaly detector
AnomalyDetector	None	anomaly detector used by the predictor
FeatureExtractor	Identity	how to extract features from which to learn
FeatureNames	Automatic	feature names to assign for input data
FeatureTypes	Automatic	feature types to assume for input data
IndeterminateThreshold	0	below what probability density to return Indeterminate
InitialEvaluationHistory	None	initial set of configurations and values
MaxIterations	2000	maximum number of iterations
Method	Automatic	method used to determine configurations to query and the prediction algorithm to use
MissingValueSynthesis	Automatic	how to synthesize missing values
PerformanceGoal	Automatic	aspects of performance to try to optimize
RandomSeeding	1234	what seeding of pseudorandom generators should be done internally
RecalibrationFunction	Automatic	how to post-process predicted value
TargetDevice	"CPU"	the target device on which to perform training
TimeGoal	Automatic	how long to spend training the classifier
TrainingProgressReporting	Automatic	how to report progress during training
UtilityFunction	Automatic	utility as function of actual and predicted value
ValidationSet	Automatic	data on which to validate the model generated

Examples

open allclose all

Basic Examples (3)Summary of the most common use cases

Train an ActivePredictionObject[…] to find the predictor for a function, given a set of configurations:

In[1]:=1

✖

https://wolfram.com/xid/0g7h9woqf92-eamr7q

Out[1]=1

Extract the resulting predictor:

In[2]:=2

✖

https://wolfram.com/xid/0g7h9woqf92-fz55mq

Out[2]=2

Predict new examples:

In[3]:=3

✖

https://wolfram.com/xid/0g7h9woqf92-jr7hzm

Out[3]=3

Train a prediction object to find the predictor for a function whose domain is defined by an interval:

In[1]:=1

✖

https://wolfram.com/xid/0g7h9woqf92-71unuc

Out[1]=1

Extract the predictor:

In[2]:=2

✖

https://wolfram.com/xid/0g7h9woqf92-v5ek5c

Out[2]=2

Predict new examples:

In[3]:=3

✖

https://wolfram.com/xid/0g7h9woqf92-prwr5

Out[3]=3

Train a prediction object to find the predictor for the Det function, with the domain defined by a configuration generator:

In[1]:=1

✖

https://wolfram.com/xid/0g7h9woqf92-p9xt0c

Out[1]=1

Extract the predictor:

In[2]:=2

✖

https://wolfram.com/xid/0g7h9woqf92-vequm4

Out[2]=2

Predict new examples:

In[3]:=3

✖

https://wolfram.com/xid/0g7h9woqf92-vzz0e1

Out[3]=3

Scope (3)Survey of the scope of standard use cases

Train a prediction object to find a predictor for the sine function in an interval:

In[1]:=1

✖

https://wolfram.com/xid/0g7h9woqf92-pgt7ug

Out[1]=1

Obtain the list of available object properties:

In[2]:=2

✖

https://wolfram.com/xid/0g7h9woqf92-39v469

Out[2]=2

Obtain the history of explored configurations:

In[3]:=3

✖

https://wolfram.com/xid/0g7h9woqf92-fxrok9

Out[3]=3

Obtain the predictors trained during active prediction, along with some of their properties:

In[4]:=4

✖

https://wolfram.com/xid/0g7h9woqf92-4wyf4u

Out[4]=4

Obtain the final predictor:

In[5]:=5

✖

https://wolfram.com/xid/0g7h9woqf92-53v9i0

Out[5]=5

Obtain the method used to choose configurations to add to the training set:

In[6]:=6

✖

https://wolfram.com/xid/0g7h9woqf92-pwngyv

Out[6]=6

Obtain some other properties:

In[7]:=7

✖

https://wolfram.com/xid/0g7h9woqf92-hw4p4y

Out[7]=7

Display the performances of the predictors trained during active prediction:

In[8]:=8

✖

https://wolfram.com/xid/0g7h9woqf92-e88e20

Out[8]=8

Visualize the predictions of the predictor on new examples:

In[9]:=9

✖

https://wolfram.com/xid/0g7h9woqf92-v3b645

Out[9]=9

Train a prediction object to find the predictor for a function that computes the color distance between a given color and the red color, with the domain defined by a random color generator:

In[1]:=1

✖

https://wolfram.com/xid/0g7h9woqf92-jmsr2p

Out[1]=1

Obtain the predictor:

In[2]:=2

✖

https://wolfram.com/xid/0g7h9woqf92-3bfsuz

Out[2]=2

Display the performances of the predictors trained during active prediction:

In[3]:=3

✖

https://wolfram.com/xid/0g7h9woqf92-6nk7qk

Out[3]=3

Display the comparison plot of the predictor for a test set:

In[4]:=4

✖

https://wolfram.com/xid/0g7h9woqf92-2z3ar7

Out[4]=4

Define a nontrivial function, with the domain defined by a neighborhood configuration generator:

In[1]:=1

✖

https://wolfram.com/xid/0g7h9woqf92-b4xhzs

Train a prediction object to find a predictor for the function, starting with some initial configurations:

In[2]:=2

✖

https://wolfram.com/xid/0g7h9woqf92-srmmdp

Out[2]=2

Obtain the predictor:

In[3]:=3

✖

https://wolfram.com/xid/0g7h9woqf92-xf2y34

Out[3]=3

Visualize the predictions of the predictor. It provides a good model of the function in the neighborhood of the initial configurations:

In[4]:=4

✖

https://wolfram.com/xid/0g7h9woqf92-4c964f

Out[4]=4

Options (3)Common values & functionality for each option

InitialEvaluationHistory (1)

Define a quadratic function whose domain is defined by a set of numbers:

In[1]:=1

✖

https://wolfram.com/xid/0g7h9woqf92-y5pitz

Construct an initial "training set":

In[2]:=2

✖

https://wolfram.com/xid/0g7h9woqf92-lq60o2

Out[2]=2

Train a prediction object to find a predictor for the function using the preceding information:

In[3]:=3

✖

https://wolfram.com/xid/0g7h9woqf92-7z9qmw

Out[3]=3

The examples in the first row in the training history now correspond to the initial training set:

In[4]:=4

✖

https://wolfram.com/xid/0g7h9woqf92-p7ov4v

Out[4]=4

MaxIterations (1)

Define a nontrivial two-dimensional function:

In[1]:=1

✖

https://wolfram.com/xid/0g7h9woqf92-gm2570

Train a prediction object to find a predictor for the function within a unit disk:

In[2]:=2

✖

https://wolfram.com/xid/0g7h9woqf92-uu6pnh

Out[2]=2

Obtain the number of function evaluations:

In[3]:=3

✖

https://wolfram.com/xid/0g7h9woqf92-e6zvcs

Out[3]=3

Specify the maximum number of iterations:

In[4]:=4

✖

https://wolfram.com/xid/0g7h9woqf92-zbusip

Out[4]=4

Check the number of function evaluations now:

In[5]:=5

✖

https://wolfram.com/xid/0g7h9woqf92-33s2bl

Out[5]=5

Method (1)

Define a nontrivial stochastic function:

In[1]:=1

✖

https://wolfram.com/xid/0g7h9woqf92-kezlvu

Train a prediction object by specifying the method as an association, choosing the evaluation strategy and the prediction method:

In[2]:=2

✖

https://wolfram.com/xid/0g7h9woqf92-816yfj

Out[2]=2

Obtain the predictor:

In[3]:=3

✖

https://wolfram.com/xid/0g7h9woqf92-tjldx7

Out[3]=3

Specify a different method for active prediction:

In[4]:=4

✖

https://wolfram.com/xid/0g7h9woqf92-pfpp78

Out[4]=4

Obtain the predictor again:

In[5]:=5

✖

https://wolfram.com/xid/0g7h9woqf92-qi3wxr

Out[5]=5

Visualize the predictions of the two predictors. "GaussianProcess" produces a smoother predictor relative to "NearestNeighbors":

In[6]:=6

✖

https://wolfram.com/xid/0g7h9woqf92-vym7jj

Out[6]=6

Applications (2)Sample problems that can be solved with this function

Efficiently train a model to predict the elevation at a specific location:

In[1]:=1

✖

https://wolfram.com/xid/0g7h9woqf92-ev5fs8

Sample 1000 random locations to test the quality of the model:

In[2]:=2

✖

https://wolfram.com/xid/0g7h9woqf92-movia0

Compare the predicted elevation versus the actual elevation obtained via a server call:

In[310]:=310

✖

https://wolfram.com/xid/0g7h9woqf92-tusmgm

Out[310]=310

In[12]:=12

✖

https://wolfram.com/xid/0g7h9woqf92-top3sx

Out[12]=12

LogLikelihood Function Predictor (1)

Load Fisher's Iris dataset and divide it into a training set and a test set:

In[1]:=1

✖

https://wolfram.com/xid/0g7h9woqf92-tk9bkv

Construct a LogLikelihood function that trains a classifier on the training sample and then gives the "LogLikelihoodRate" on the test sample for a given choice of the hyperparameters:

In[2]:=2

✖

https://wolfram.com/xid/0g7h9woqf92-voiwbr

Train a prediction object to find a predictor for the LogLikelihood function over a rectangular domain:

In[3]:=3

✖

https://wolfram.com/xid/0g7h9woqf92-uju1q0

Out[3]=3

Obtain the predictor:

In[4]:=4

✖

https://wolfram.com/xid/0g7h9woqf92-6078dm

Out[4]=4

Obtain the coordinates of the explored configurations and their values:

In[5]:=5

✖

https://wolfram.com/xid/0g7h9woqf92-jvcnbp

Visualize the prediction of the predictor together with the explored configurations:

In[6]:=6

✖

https://wolfram.com/xid/0g7h9woqf92-7lxq6e

Out[6]=6

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ActivePrediction

Details and Options

List of all options

Examples

Basic Examples (3)Summary of the most common use cases

Scope (3)Survey of the scope of standard use cases