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Implements the Tsetlin Machine, Convolutional Tsetlin Machine, Regression Tsetlin Machine, and Weighted Tsetlin Machine, with support for continuous features, multigranularity, and clause indexing
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README.md

pyTsetlinMachine

Implementation of the Tsetlin Machine (https://arxiv.org/abs/1804.01508), Convolutional Tsetlin Machine (https://arxiv.org/abs/1905.09688), Regression Tsetlin Machine (https://arxiv.org/abs/1905.04206, https://link.springer.com/chapter/10.1007/978-3-030-30244-3_23), and Weighted Tsetlin Machine (https://arxiv.org/abs/1911.12607), with support for continuous features (https://arxiv.org/abs/1905.04199, https://link.springer.com/chapter/10.1007%2F978-3-030-22999-3_49), multigranular clauses (https://arxiv.org/abs/1909.07310, https://link.springer.com/chapter/10.1007/978-3-030-34885-4_11), and clause indexing.

Installation

pip install pyTsetlinMachine

Documentation

Documentation coming soon at https://pytsetlinmachine.readthedocs.io/en/latest/

Multi-threading

Multi-threaded implementation, https://github.com/cair/pyTsetlinMachineParallel

Tutorials

Convolutional Tsetlin Machine tutorial, https://github.com/cair/convolutional-tsetlin-machine

Examples

Multiclass Demo

Code: NoisyXORDemo.py

from pyTsetlinMachine.tm import MultiClassTsetlinMachine
import numpy as np 

train_data = np.loadtxt("NoisyXORTrainingData.txt")
X_train = train_data[:,0:-1]
Y_train = train_data[:,-1]

test_data = np.loadtxt("NoisyXORTestData.txt")
X_test = test_data[:,0:-1]
Y_test = test_data[:,-1]

tm = MultiClassTsetlinMachine(10, 15, 3.9, boost_true_positive_feedback=0)

tm.fit(X_train, Y_train, epochs=200)

print("Accuracy:", 100*(tm.predict(X_test) == Y_test).mean())

print("Prediction: x1 = 1, x2 = 0, ... -> y = %d" % (tm.predict(np.array([[1,0,1,0,1,0,1,1,1,1,0,0]]))))
print("Prediction: x1 = 0, x2 = 1, ... -> y = %d" % (tm.predict(np.array([[0,1,1,0,1,0,1,1,1,1,0,0]]))))
print("Prediction: x1 = 0, x2 = 0, ... -> y = %d" % (tm.predict(np.array([[0,0,1,0,1,0,1,1,1,1,0,0]]))))
print("Prediction: x1 = 1, x2 = 1, ... -> y = %d" % (tm.predict(np.array([[1,1,1,0,1,0,1,1,1,1,0,0]]))))

Output

python3 ./NoisyXORDemo.py 

Accuracy: 100.00%

Prediction: x1 = 1, x2 = 0, ... -> y = 1
Prediction: x1 = 0, x2 = 1, ... -> y = 1
Prediction: x1 = 0, x2 = 0, ... -> y = 0
Prediction: x1 = 1, x2 = 1, ... -> y = 0

Interpretability Demo

Code: InterpretabilityDemo.py

from pyTsetlinMachine.tm import MultiClassTsetlinMachine
import numpy as np 

number_of_features = 20
noise = 0.1

X_train = np.random.randint(0, 2, size=(5000, number_of_features), dtype=np.uint32)
Y_train = np.logical_xor(X_train[:,0], X_train[:,1]).astype(dtype=np.uint32)
Y_train = np.where(np.random.rand(5000) <= noise, 1-Y_train, Y_train) # Adds noise

X_test = np.random.randint(0, 2, size=(5000, number_of_features), dtype=np.uint32)
Y_test = np.logical_xor(X_test[:,0], X_test[:,1]).astype(dtype=np.uint32)

tm = MultiClassTsetlinMachine(10, 15, 3.0, boost_true_positive_feedback=0)

tm.fit(X_train, Y_train, epochs=200)

print("Accuracy:", 100*(tm.predict(X_test) == Y_test).mean())

print("\nClass 0 Positive Clauses:\n")
for j in range(0, 10, 2):
	print("Clause #%d: " % (j), end=' ')
	l = []
	for k in range(number_of_features*2):
		if tm.ta_action(0, j, k) == 1:
			if k < number_of_features:
				l.append(" x%d" % (k))
			else:
				l.append("¬x%d" % (k-number_of_features))
	print("".join(l))

print("\nClass 0 Negative Clauses:\n")
for j in range(1, 10, 2):
	print("Clause #%d: " % (j), end=' ')
	l = []
	for k in range(number_of_features*2):
		if tm.ta_action(0, j, k) == 1:
			if k < number_of_features:
				l.append(" x%d" % (k))
			else:
				l.append("¬x%d" % (k-number_of_features))
	print("".join(l))

print("\nClass 1 Positive Clauses:\n")
for j in range(0, 10, 2):
	print("Clause #%d: " % (j), end=' ')
	l = []
	for k in range(number_of_features*2):
		if tm.ta_action(1, j, k) == 1:
			if k < number_of_features:
				l.append(" x%d" % (k))
			else:
				l.append("¬x%d" % (k-number_of_features))
	print("".join(l))

print("\nClass 1 Negative Clauses:\n")
for j in range(1, 10, 2):
	print("Clause #%d: " % (j), end=' ')
	l = []
	for k in range(number_of_features*2):
		if tm.ta_action(1, j, k) == 1:
			if k < number_of_features:
				l.append(" x%d" % (k))
			else:
				l.append("¬x%d" % (k-number_of_features))
	print("".join(l))

Output

python3 ./InterpretabilityDemo.py

Accuracy: 100.0

Class 0 Positive Clauses:

Clause #0:  ¬x0 ∧ ¬x1
Clause #2:   x0 ∧  x1
Clause #4:   x0 ∧  x1
Clause #6:  ¬x0 ∧ ¬x1
Clause #8:  ¬x0 ∧ ¬x1

Class 0 Negative Clauses:

Clause #1:   x0 ∧ ¬x1
Clause #3:   x0 ∧ ¬x1
Clause #5:   x1 ∧ ¬x0
Clause #7:   x1 ∧ ¬x0
Clause #9:   x0 ∧ ¬x1

Class 1 Positive Clauses:

Clause #0:   x1 ∧ ¬x0
Clause #2:   x1 ∧ ¬x0
Clause #4:   x0 ∧ ¬x1
Clause #6:   x0 ∧ ¬x1
Clause #8:   x0 ∧ ¬x1

Class 1 Negative Clauses:

Clause #1:   x0 ∧  x1
Clause #3:  ¬x0 ∧ ¬x1
Clause #5:  ¬x0 ∧ ¬x1
Clause #7:  ¬x0 ∧ ¬x1
Clause #9:   x0 ∧  x1

2D Convolution Demo

Code: 2DNoisyXORDemo.py

from pyTsetlinMachine.tm import MultiClassConvolutionalTsetlinMachine2D
import numpy as np 

train_data = np.loadtxt("2DNoisyXORTrainingData.txt")
X_train = train_data[:,0:-1].reshape(train_data.shape[0], 4, 4)
Y_train = train_data[:,-1]

test_data = np.loadtxt("2DNoisyXORTestData.txt")
X_test = test_data[:,0:-1].reshape(test_data.shape[0], 4, 4)
Y_test = test_data[:,-1]

ctm = MultiClassConvolutionalTsetlinMachine2D(40, 60, 3.9, (2, 2), boost_true_positive_feedback=0)

ctm.fit(X_train, Y_train, epochs=5000)

print("Accuracy:", 100*(ctm.predict(X_test) == Y_test).mean())

Xi = np.array([[[0,1,1,0],
		[1,1,0,1],
		[1,0,1,1],
		[0,0,0,1]]])

print("\nInput Image:\n")
print(Xi)
print("\nPrediction: %d" % (ctm.predict(Xi)))

Output

python3 ./2DNoisyXORDemo.py 

Accuracy: 99.97%

Input Image:

[[0 1 1 0]
 [1 1 0 1]
 [1 0 1 1]
 [0 0 0 1]]

Prediction: 1

Continuous Input Demo

Code: BreastCancerDemo.py

from pyTsetlinMachine.tm import MultiClassTsetlinMachine
from pyTsetlinMachine.tools import Binarizer
import numpy as np

from sklearn import datasets
from sklearn.model_selection import train_test_split

breast_cancer = datasets.load_breast_cancer()
X = breast_cancer.data
Y = breast_cancer.target

b = Binarizer(max_bits_per_feature = 10)
b.fit(X)
X_transformed = b.transform(X)

tm = MultiClassTsetlinMachine(800, 40, 5.0)

print("\nMean accuracy over 100 runs:\n")
tm_results = np.empty(0)
for i in range(100):
	X_train, X_test, Y_train, Y_test = train_test_split(X_transformed, Y, test_size=0.2)

	tm.fit(X_train, Y_train, epochs=25)
	tm_results = np.append(tm_results, np.array(100*(tm.predict(X_test) == Y_test).mean()))
	print("#%d Average Accuracy: %.2f%% +/- %.2f" % (i+1, tm_results.mean(), 1.96*tm_results.std()/np.sqrt(i+1)))

Output

python3 ./BreastCancerDemo.py 

Mean accuracy over 100 runs:

#1 Average Accuracy: 97.37% +/- 0.00
#2 Average Accuracy: 97.37% +/- 0.00
...
#99 Average Accuracy: 97.52% +/- 0.29
#100 Average Accuracy: 97.54% +/- 0.29

MNIST Demo

Code: MNISTDemo.py

from pyTsetlinMachine.tm import MultiClassTsetlinMachine
import numpy as np
from time import time

from keras.datasets import mnist

(X_train, Y_train), (X_test, Y_test) = mnist.load_data()

X_train = np.where(X_train.reshape((X_train.shape[0], 28*28)) > 75, 1, 0) 
X_test = np.where(X_test.reshape((X_test.shape[0], 28*28)) > 75, 1, 0) 

tm = MultiClassTsetlinMachine(2000, 50, 10.0)

print("\nAccuracy over 250 epochs:\n")
for i in range(250):
	start_training = time()
	tm.fit(X_train, Y_train, epochs=1, incremental=True)
	stop_training = time()

	start_testing = time()
	result = 100*(tm.predict(X_test) == Y_test).mean()
	stop_testing = time()

	print("#%d Accuracy: %.2f%% Training: %.2fs Testing: %.2fs" % (i+1, result, stop_training-start_training, stop_testing-start_testing))

Output

python3 ./MNISTDemo.py 

Accuracy over 250 epochs:

#1 Accuracy: 94.63% Training: 42.75s Testing: 3.06s
#2 Accuracy: 95.52% Training: 23.05s Testing: 3.12s
#3 Accuracy: 95.97% Training: 20.13s Testing: 3.07s
...

#248 Accuracy: 98.06% Training: 7.77s Testing: 3.09s
#249 Accuracy: 97.98% Training: 7.74s Testing: 3.10s
#250 Accuracy: 98.07% Training: 7.92s Testing: 3.12s

MNIST Demo w/Weighted Clauses

Code: MNISTDemoWeightedClauses.py

from pyTsetlinMachine.tm import MultiClassTsetlinMachine
import numpy as np
from time import time

from keras.datasets import mnist

(X_train, Y_train), (X_test, Y_test) = mnist.load_data()

X_train = np.where(X_train.reshape((X_train.shape[0], 28*28)) > 75, 1, 0) 
X_test = np.where(X_test.reshape((X_test.shape[0], 28*28)) > 75, 1, 0) 

tm = MultiClassTsetlinMachine(2000, 50*100, 10.0, weighted_clauses=True)

print("\nAccuracy over 60 epochs:\n")
for i in range(60):
        start_training = time()
        tm.fit(X_train, Y_train, epochs=1, incremental=True)
        stop_training = time()

        start_testing = time()
        result = 100*(tm.predict(X_test) == Y_test).mean()
        stop_testing = time()

        print("#%d Accuracy: %.2f%% Training: %.2fs Testing: %.2fs" % (i+1, result, stop_training-start_training, stop_testing-start_testing))

Output

python3 ./MNISTDemoWeightedClauses.py

Accuracy over 60 epochs:

#1 Accuracy: 93.65% Training: 60.98s Testing: 3.98s
#2 Accuracy: 95.33% Training: 26.84s Testing: 3.87s
#3 Accuracy: 96.08% Training: 22.41s Testing: 3.95s
...

#58 Accuracy: 98.14% Training: 8.54s Testing: 4.17s
#59 Accuracy: 98.08% Training: 8.49s Testing: 4.22s
#60 Accuracy: 98.19% Training: 8.80s Testing: 4.15s

MNIST 2D Convolution Demo w/Weighted Clauses

Code: MNISTDemo2DConvolutionWeightedClauses.py

from pyTsetlinMachine.tm import MultiClassConvolutionalTsetlinMachine2D
import numpy as np
from time import time

from keras.datasets import mnist

(X_train, Y_train), (X_test, Y_test) = mnist.load_data()

X_train = np.where(X_train >= 75, 1, 0) 
X_test = np.where(X_test >= 75, 1, 0) 

tm = MultiClassConvolutionalTsetlinMachine2D(2000, 50*100, 5.0, (10, 10), weighted_clauses=True)

print("\nAccuracy over 30 epochs:\n")
for i in range(30):
	start = time()
	tm.fit(X_train, Y_train, epochs=1, incremental=True)
	stop = time()
	
	result = 100*(tm.predict(X_test) == Y_test).mean()
	
	print("#%d Accuracy: %.2f%% (%.2fs)" % (i+1, result, stop-start))

Output

python3 ./MNISTDemo2DConvolutionWeightedClauses.py 

Accuracy over 30 epochs:

#1 Accuracy: 97.53% (403.06s)
#2 Accuracy: 98.07% (421.25s)
#3 Accuracy: 98.36% (430.48s)
...

#28 Accuracy: 99.14% (540.11s)
#29 Accuracy: 99.21% (546.38s)
#30 Accuracy: 99.16% (538.87s)

Fashion MNIST 2D Convolution Demo w/Weighted Clauses

Code: FashionMNISTDemo2DConvolutionWeightedClauses.py

from pyTsetlinMachine.tm import MultiClassConvolutionalTsetlinMachine2D
import numpy as np
from time import time
import cv2
from keras.datasets import fashion_mnist

(X_train, Y_train), (X_test, Y_test) = fashion_mnist.load_data()
X_train = np.copy(X_train)
X_test = np.copy(X_test)

for i in range(X_train.shape[0]):
	X_train[i,:] = cv2.adaptiveThreshold(X_train[i], 1, cv2.ADAPTIVE_THRESH_GAUSSIAN_C, cv2.THRESH_BINARY, 11, 2)

for i in range(X_test.shape[0]):
	X_test[i,:] = cv2.adaptiveThreshold(X_test[i], 1, cv2.ADAPTIVE_THRESH_GAUSSIAN_C, cv2.THRESH_BINARY, 11, 2)

tm = MultiClassConvolutionalTsetlinMachine2D(2000, 50*100, 5.0, (10, 10), weighted_clauses=True)

print("\nAccuracy over 30 epochs:\n")
for i in range(30):
	start = time()
	tm.fit(X_train, Y_train, epochs=1, incremental=True)
	stop = time()
	
	result = 100*(tm.predict(X_test) == Y_test).mean()
	
	print("#%d Accuracy: %.2f%% (%.2fs)" % (i+1, result, stop-start))

Output

python3 ./FashionMNISTDemo2DConvolutionWeightedClauses.py 

Accuracy over 30 epochs:

#1 Accuracy: 85.25% (615.68s)
#2 Accuracy: 86.60% (615.83s)
#3 Accuracy: 87.56% (607.37s)
...

#28 Accuracy: 90.14% (759.22s)
#29 Accuracy: 90.39% (564.35s)
#30 Accuracy: 90.06% (560.08s)

IMDb Text Categorization Demo

Code: IMDbTextCategorizationDemo.py

import numpy as np
import keras
from sklearn.feature_selection import SelectKBest
from sklearn.feature_selection import chi2
from keras.datasets import imdb
from pyTsetlinMachine.tm import MultiClassTsetlinMachine
from time import time

MAX_NGRAM = 2

NUM_WORDS=5000
INDEX_FROM=2 

FEATURES=5000

print("Downloading dataset...")

train,test = keras.datasets.imdb.load_data(num_words=NUM_WORDS, index_from=INDEX_FROM)

train_x,train_y = train
test_x,test_y = test

word_to_id = keras.datasets.imdb.get_word_index()
word_to_id = {k:(v+INDEX_FROM) for k,v in word_to_id.items()}
word_to_id["<PAD>"] = 0
word_to_id["<START>"] = 1
word_to_id["<UNK>"] = 2

print("Producing bit representation...")

# Produce N-grams

id_to_word = {value:key for key,value in word_to_id.items()}

vocabulary = {}
for i in range(train_y.shape[0]):
	terms = []
	for word_id in train_x[i]:
		terms.append(id_to_word[word_id])
	
	for N in range(1,MAX_NGRAM+1):
		grams = [terms[j:j+N] for j in range(len(terms)-N+1)]
		for gram in grams:
			phrase = " ".join(gram)
			
			if phrase in vocabulary:
				vocabulary[phrase] += 1
			else:
				vocabulary[phrase] = 1

# Assign a bit position to each N-gram (minimum frequency 10) 

phrase_bit_nr = {}
bit_nr_phrase = {}
bit_nr = 0
for phrase in vocabulary.keys():
	if vocabulary[phrase] < 10:
		continue

	phrase_bit_nr[phrase] = bit_nr
	bit_nr_phrase[bit_nr] = phrase
	bit_nr += 1

# Create bit representation

X_train = np.zeros((train_y.shape[0], len(phrase_bit_nr)), dtype=np.uint32)
Y_train = np.zeros(train_y.shape[0], dtype=np.uint32)
for i in range(train_y.shape[0]):
	terms = []
	for word_id in train_x[i]:
		terms.append(id_to_word[word_id])

	for N in range(1,MAX_NGRAM+1):
		grams = [terms[j:j+N] for j in range(len(terms)-N+1)]
		for gram in grams:
			phrase = " ".join(gram)
			if phrase in phrase_bit_nr:
				X_train[i,phrase_bit_nr[phrase]] = 1

	Y_train[i] = train_y[i]

X_test = np.zeros((test_y.shape[0], len(phrase_bit_nr)), dtype=np.uint32)
Y_test = np.zeros(test_y.shape[0], dtype=np.uint32)

for i in range(test_y.shape[0]):
	terms = []
	for word_id in test_x[i]:
		terms.append(id_to_word[word_id])

	for N in range(1,MAX_NGRAM+1):
		grams = [terms[j:j+N] for j in range(len(terms)-N+1)]
		for gram in grams:
			phrase = " ".join(gram)
			if phrase in phrase_bit_nr:
				X_test[i,phrase_bit_nr[phrase]] = 1				

	Y_test[i] = test_y[i]

print("Selecting features...")

SKB = SelectKBest(chi2, k=FEATURES)
SKB.fit(X_train, Y_train)

selected_features = SKB.get_support(indices=True)
X_train = SKB.transform(X_train)
X_test = SKB.transform(X_test)

tm = MultiClassTsetlinMachine(10000, 80, 27.0)

print("\nAccuracy over 50 epochs:\n")
for i in range(50):
	start_training = time()
	tm.fit(X_train, Y_train, epochs=1, incremental=True)
	stop_training = time()

	start_testing = time()
	result = 100*(tm.predict(X_test) == Y_test).mean()
	stop_testing = time()

	print("#%d Accuracy: %.2f%% Training: %.2fs Testing: %.2fs" % (i+1, result, stop_training-start_training, stop_testing-start_testing))

Output:

python ./IMDbTextCategorizationDemo.py

Downloading dataset...
Producing bit representation...
Selecting features...

Accuracy over 50 epochs:

#1 Accuracy: 86.84% Training: 947.15s Testing: 12.39s
#2 Accuracy: 87.62% Training: 709.67s Testing: 11.34s
#3 Accuracy: 88.05% Training: 631.41s Testing: 13.11s
...

#48 Accuracy: 89.56% Training: 357.80s Testing: 9.59s
#49 Accuracy: 89.50% Training: 354.74s Testing: 9.58s
#50 Accuracy: 89.45% Training: 371.62s Testing: 9.67s

Regression Demo

Code: RegressionDemo.py

from pyTsetlinMachine.tm import RegressionTsetlinMachine
from pyTsetlinMachine.tools import Binarizer
import numpy as np
from time import time

from sklearn import datasets
from sklearn.model_selection import train_test_split

california_housing = datasets.fetch_california_housing()
X = california_housing.data
Y = california_housing.target

b = Binarizer(max_bits_per_feature = 10)
b.fit(X)
X_transformed = b.transform(X)

tm = RegressionTsetlinMachine(1000, 500*10, 2.75, weighted_clauses=True)

print("\nRMSD over 25 runs:\n")
tm_results = np.empty(0)
for i in range(25):
	X_train, X_test, Y_train, Y_test = train_test_split(X_transformed, Y)

	start = time()
	tm.fit(X_train, Y_train, epochs=30)
	stop = time()
	tm_results = np.append(tm_results, np.sqrt(((tm.predict(X_test) - Y_test)**2).mean()))

	print("#%d RMSD: %.2f +/- %.2f (%.2fs)" % (i+1, tm_results.mean(), 1.96*tm_results.std()/np.sqrt(i+1), stop-start))

Output

python3 ./RegressionDemo.py 

RMSD over 25 runs:

#1 RMSD: 0.62 +/- 0.00 (13.17s)
#2 RMSD: 0.61 +/- 0.01 (13.19s)
...

#24 RMSD: 0.61 +/- 0.00 (13.65s)
#25 RMSD: 0.61 +/- 0.00 (13.73s)

Further Work

  • Multilayer Tsetlin Machine
  • Recurrent Tsetlin Machine
  • GPU support
  • Optimize convolution code
  • More extensive hyper-parameter search for the demos

Requirements

Acknowledgements

I thank my colleagues from the Centre for Artificial Intelligence Research (CAIR), Lei Jiao, Xuan Zhang, Geir Thore Berge, Darshana Abeyrathna, Saeed Rahimi Gorji, Sondre Glimsdal, Rupsa Saha, Bimal Bhattarai, Rohan K. Yadev, Bernt Viggo Matheussen, Morten Goodwin, Christian Omlin, Vladimir Zadorozhny (University of Pittsburgh), Jivitesh Sharma, and Ahmed Abouzeid, for their contributions to the development of the Tsetlin machine family of techniques. I would also like to thank our House of CAIR partners, Alex Yakovlev, Rishad Shafik, Adrian Wheeldon, Jie Lei, Tousif Rahman (Newcastle University), Jonny Edwards (Temporal Computing), Marco Wiering (University of Groningen), Adrian Phoulady, Anders Refsdal Olsen, Halvor Smørvik, and Erik Mathisen for their many contributions.

Citation

@InProceedings{phoulady2019weighted, 
  author={Adrian {Phoulady} and Ole-Christoffer {Granmo} and Saeed Rahimi {Gorji} and Hady Ahmady {Phoulady}}, 
  booktitle={To Appear in the Proceedings of the Ninth International Workshop on Statistical Relational AI (StarAI 2020)}, 
  title="{The Weighted Tsetlin Machine: Compressed Representations with Clause Weighting}",
  year={2020}
}
@article{abeyrathna2019nonlinear, 
  author={K. Darshana {Abeyrathna} and Ole-Christoffer {Granmo} and Xuan {Zhang} and Lei {Jiao} and Morten {Goodwin}}, 
  journal={To Appear in Philosophical Transactions of the Royal Society A},
  title="{The Regression Tsetlin Machine - A Novel Approach to Interpretable Non-Linear Regression}",
  year={2019}
}
@InProceedings{gorji2019multigranular,
  author = {Saeed Rahimi {Gorji} and Ole-Christoffer {Granmo} and Adrian {Phoulady} and Morten {Goodwin}},
  title = "{A Tsetlin Machine with Multigranular Clauses}",
  booktitle="Lecture Notes in Computer Science: Proceedings of the Thirty-ninth International Conference on Innovative Techniques and Applications of Artificial Intelligence (SGAI-2019)", year="2019",
  volume = {11927},
  publisher="Springer International Publishing"
}
@article{berge2019text, 
  author={Geir Thore {Berge} and Ole-Christoffer {Granmo} and Tor Oddbjørn {Tveit} and Morten {Goodwin} and Lei {Jiao} and Bernt Viggo {Matheussen}}, 
  journal={IEEE Access}, 
  title="{Using the Tsetlin Machine to Learn Human-Interpretable Rules for High-Accuracy Text Categorization with Medical Applications}",
  volume={7},
  pages={115134-115146}, 
  year={2019}, 
  doi={10.1109/ACCESS.2019.2935416}, 
  ISSN={2169-3536}
}
@article{granmo2019convtsetlin,
  author = {{Granmo}, Ole-Christoffer and {Glimsdal}, Sondre and {Jiao}, Lei and {Goodwin}, Morten and {Omlin}, Christian W. and {Berge}, Geir Thore},
  title = "{The Convolutional Tsetlin Machine}",
  journal = {arXiv preprint arXiv:1905.09688}, year = {2019}
}
@InProceedings{abeyrathna2019regressiontsetlin,
  author = {{Abeyrathna}, Kuruge Darshana and {Granmo}, Ole-Christoffer and {Jiao}, Lei and {Goodwin}, Morten},
  title = "{The Regression Tsetlin Machine: A Tsetlin Machine for Continuous Output Problems}",
  editor="Moura Oliveira, Paulo and Novais, Paulo and Reis, Lu{\'i}s Paulo ",
  booktitle="Progress in Artificial Intelligence", year="2019",
  publisher="Springer International Publishing",
  pages="268--280"
}
@InProceedings{abeyrathna2019continuousinput,
  author = {{Abeyrathna}, Kuruge Darshana and {Granmo}, Ole-Christoffer and {Zhang}, Xuan and {Goodwin}, Morten},
  title = "{A Scheme for Continuous Input to the Tsetlin Machine with Applications to Forecasting Disease Outbreaks}",
  booktitle = "{Advances and Trends in Artificial Intelligence. From Theory to Practice}", year = "2019",
  editor = "Wotawa, Franz and Friedrich, Gerhard and Pill, Ingo and Koitz-Hristov, Roxane and Ali, Moonis",
  publisher = "Springer International Publishing",
  pages = "564--578"
}
@article{granmo2018tsetlin,
  author = {{Granmo}, Ole-Christoffer},
  title = "{The Tsetlin Machine - A Game Theoretic Bandit Driven Approach to Optimal Pattern Recognition with Propositional Logic}",
  journal = {arXiv preprint arXiv:1804.01508}, year = {2018}
}

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Copyright (c) 2019 Ole-Christoffer Granmo

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