Machine-learning techniques involving monotonic recurrent neural networks
Various aspects involve a monotonic recurrent neural network (MRNN) trained for risk assessment or other purposes. For instance, the MRNN is trained to compute a risk indicator from a predictor variable. Training the MRNN includes adjusting weights of nodes of the MRNN subject to a set of monotonicity constraints, wherein the set of monotonicity constraints causes output risk indicators computed by the RNN to be a monotonic function of input predictor variables. The trained monotonic RNN can be used to generate an output risk indicator for a target entity.
1 . A system comprising:
a first computing system configured for:
receiving, from a second computing system, a risk assessment query that identifies a target entity,
providing a predictor variable for the target entity to a recurrent neural network (RNN),
computing, with the RNN, an output risk indicator from the predictor variable, the RNN having one or more layers of nodes that are interconnected, the nodes comprising one or more hidden states having stored values based on predictor values in the predictor variable, the nodes having weights causing output risk indicators of the RNN to be a monotonic function of input predictor variables that are input into the RNN,
wherein a loss function of the RNN includes a mapping function for adjusting one or more of the weights of the nodes of the RNN, wherein the mapping function adjusts the weights of the nodes during training to minimize the loss function of the RNN subject to a set of monotonicity constraints comprising (i) a set of activation functions with derivatives that are nonnegative and (ii) a set of nonnegative weight matrices in which at least one weight value of at least one weight matrix is adjusted by the mapping function during the training, and
transmitting the output risk indicator to the second computing system; and
the second computing system, wherein the second computing system is communicatively coupled to the first computing system and is configured for controlling, based on the output risk indicator, access by the target entity to one or more interactive computing environments.
2 . The system of claim 1 , wherein the first computing system is further configured for training the RNN by performing training operations comprising:
accessing training samples comprising training predictor variables and training risk indicators corresponding to the training predictor variables; and
adjusting the weights of the nodes of the RNN subject to the set of monotonicity constraints, wherein the set of monotonicity constraints causes the output risk indicators computed by the RNN to be a monotonic function of the input predictor variables that are input into the RNN.
3 . The system of claim 2 , the training operations further comprising:
computing, with the RNN, an updated value of an updated hidden state of the one or more hidden states as a first activation function of the set of activation functions applied to a first function, the first function comprising (i) a first weight matrix of the set of nonnegative weight matrices multiplied by the predictor variable for the target entity and (ii) a second weight matrix of the set of nonnegative weight matrices multiplied by a stored value of a hidden state of the one or more hidden states,
wherein adjusting the weights of the nodes of the RNN to minimize the loss function of the RNN subject to the set of monotonicity constraints comprises:
adjusting first weight values in the first weight matrix, wherein each cell of the first weight matrix is nonnegative, and
adjusting second weight values in the second weight matrix, wherein each cell of the second weight matrix is nonnegative.
4 . The system of claim 3 , wherein computing, with the RNN, the output risk indicator from the predictor variable comprises computing the output risk indicator as a second activation function of the set of activation functions of the RNN applied to a second function, the second function comprising a third weight matrix of the set of nonnegative weight matrices multiplied by the updated value of the updated hidden state,
wherein adjusting the weights of the nodes of the RNN to minimize the loss function of the RNN subject to the set of monotonicity constraints further comprises adjusting third weight values in the third weight matrix, wherein each cell of the third weight matrix is nonnegative.
5 . The system of claim 4 , wherein:
the first activation function has a respective derivative that is always nonnegative; and
the second activation function has an additional respective derivative that is always nonnegative.
6 . The system of claim 4 , wherein:
the first activation function has a respective range that is strictly nonnegative; and
the second activation function has an additional respective range that is strictly nonnegative.
7 . The system of claim 1 , wherein the RNN is a long short-term memory (LSTM) network.
8 . A method in which one or more processing devices perform operations comprising:
training a recurrent neural network (RNN) to compute a risk indicator from a predictor variable, wherein the RNN comprises one or more layers of nodes that are interconnected, the nodes comprising one or more hidden states having stored values based on predictor values in the predictor variable,
wherein training the RNN comprises:
accessing training samples comprising training predictor variables and training risk indicators corresponding to the training predictor variables; and
adjusting weights of the nodes of the RNN subject to a set of monotonicity constraints, wherein the set of monotonicity constraints causes output risk indicators computed by the RNN to be a monotonic function of input predictor variables that are input into the RNN,
wherein a loss function of the RNN includes a mapping function for adjusting one or more of the weights of the nodes of the RNN, wherein the mapping function adjusts the weights of the nodes to minimize the loss function of the RNN subject to the set of monotonicity constraints comprising (i) a set of activation functions with derivatives that are nonnegative and (ii) a set of nonnegative weight matrices in which at least one weight value of at least one weight matrix is adjusted by the mapping function during training; and
computing, responsive to a risk assessment query for a target entity, an output risk indicator for the target entity by applying the RNN to an input predictor variable associated with the target entity, wherein the output risk indicator is usable for controlling access by the target entity to one or more interactive computing environments.
9 . The method of claim 8 , the operations further comprising:
computing, by the RNN, an updated value of an updated hidden state of the one or more hidden states as a first activation function of the set of activation functions applied to a first function, the first function comprising (i) a first weight matrix of the set of nonnegative weight matrices multiplied by the input predictor variable associated with the target entity and (ii) a second weight matrix of the set of nonnegative weight matrices multiplied by a stored value of a hidden state of the one or more hidden states,
wherein adjusting the weights of the nodes of the RNN subject to the set of monotonicity constraints comprises:
adjusting first weight values in the first weight matrix, wherein each cell of the first weight matrix is nonnegative, and
adjusting second weight values in the second weight matrix, wherein each cell of the second weight matrix is nonnegative.
10 . The method of claim 9 , wherein computing, by the RNN, the output risk indicator for the target entity comprises computing the output risk indicator as a second activation function of the set of activation functions applied to a second function, the second function comprising a third weight matrix of the set of nonnegative weight matrices multiplied by the updated value of the updated hidden state,
wherein adjusting the weights of the nodes of the RNN subject to the set of monotonicity constraints further comprises adjusting third weight values in the third weight matrix, wherein each cell of the third weight matrix is nonnegative.
11 . The method of claim 10 , wherein adjusting the weights of the nodes of the RNN subject to the set of monotonicity constraints further comprises processing the training samples in mini-batches to adjust the weights of the nodes.
12 . The method of claim 10 , wherein adjusting the weights of the nodes of the RNN subject to the set of monotonicity constraints further comprises updating the first weight values of the first weight matrix, the second weight values of the second matrix, and the third weight values of the third matrix using an exponential function.
13 . The method of claim 10 , wherein:
the first activation function has a respective derivative that is always nonnegative; and
the second activation function has an additional respective derivative that is always nonnegative.
14 . The method of claim 10 , wherein:
the first activation function has a respective range that is strictly nonnegative; and
the second activation function has an additional respective range that is strictly nonnegative.
15 . The method of claim 8 , wherein the RNN is a long short-term memory (LSTM) network.
16 . A non-transitory computer-readable medium embodying program code for making a risk assessment, the program code comprising instructions that, when executed by a processor, cause the processor to perform operations comprising:
training a recurrent neural network (RNN) to compute a risk indicator from a predictor variable, wherein the RNN comprises one or more layers of nodes that are interconnected, the nodes comprising one or more hidden states having stored values based on predictor values in the predictor variable,
wherein training the RNN comprises:
accessing training samples comprising training predictor variables and training risk indicators corresponding to the training predictor variables; and
adjusting weights of the nodes of the RNN subject to a set of monotonicity constraints, wherein the set of monotonicity constraints causes output risk indicators computed by the RNN to be a monotonic function of input predictor variables that are input into the RNN,
wherein a loss function of the RNN includes a mapping function for adjusting one or more of the weights of the nodes of the RNN, wherein the mapping function adjusts the weights of the nodes to minimize the loss function of the RNN subject to the set of monotonicity constraints comprising (i) a set of activation functions with derivatives that are nonnegative and (ii) a set of nonnegative weight matrices in which at least one weight value of at least one weight matrix is adjusted by the mapping function during training; and
outputting the RNN as trained, wherein the RNN as trained is configured for computing, responsive to a risk assessment query for a target entity, an output risk indicator for the target entity by applying the RNN to an input predictor variable associated with the target entity.
17 . The non-transitory computer-readable medium of claim 16 , the operations further comprising:
computing, by the RNN, an updated value of an updated hidden state of the one or more hidden states as a first activation function of the set of activation functions applied to a first function, the first function comprising (i) a first weight matrix of the set of nonnegative weight matrices multiplied by the input predictor variable associated with the target entity and (ii) a second weight matrix of the set of nonnegative weight matrices multiplied by a stored value of a hidden state of the one or more hidden states,
wherein adjusting the weights of the nodes of the RNN subject to the set of monotonicity constraints comprises:
adjusting first weight values in the first weight matrix, wherein each cell of the first weight matrix is nonnegative, and
adjusting second weight values in the second weight matrix, wherein each cell of the second weight matrix is nonnegative.
18 . The non-transitory computer-readable medium of claim 17 , wherein the RNN as trained is further configured for computing, by the RNN, the output risk indicator for the target entity as a second activation function of the set of activation functions applied to a second function, the second function comprising a third weight matrix of the set of nonnegative weight matrices multiplied by the updated value of the updated hidden state,
wherein adjusting the weights of the nodes of the RNN subject to the set of monotonicity constraints further comprises adjusting third weight values in the third weight matrix, wherein each cell of the third weight matrix is nonnegative.
19 . The non-transitory computer-readable medium of claim 18 , wherein:
the first activation function has a respective derivative that is always nonnegative; and
the second activation function has an additional respective derivative that is always nonnegative.
20 . The non-transitory computer-readable medium of claim 18 , wherein:
the RNN is a long short-term memory (LSTM) network;
the first activation function has a respective range that is strictly nonnegative; and
the second activation function has an additional respective range that is strictly nonnegative.