DATA PROCESSING APPARATUS AND METHOD
A data processing apparatus comprises: a memory configured to store a trained model; and processing circuitry configured to: receive at least one dataset that comprises d variables and n samples; determine variances associated with the variables by processing the dataset using the model; determine an order of the variables based on the determined variances, including iteratively removing at least one node or variable represented by said at least one node thereby to determine the order.
1 . A data processing apparatus comprising:
a memory configured to store a trained model; and
processing circuitry configured to:
receive at least one dataset that comprises d variables and n samples;
determine variances associated with the variables by processing the dataset using the model;
determine an order of the variables based on the determined variances, including iteratively removing at least one node or variable represented by said at least one node thereby to determine the order.
2 . The data processing apparatus according to claim 1 , wherein the order of the variables represents an order of causation relationship(s), the variances comprise second order derivatives, and wherein a respective one of the variances is associated with each variable.
3 . The data processing apparatus according to claim 1 , wherein the determining of the variances comprises determining a variance of a second order gradient of a distribution associated with the variables.
4 . The data processing apparatus according to claim 1 , wherein the determining of the variances comprises applying a neural network, which is trained with denoising diffusion, to the dataset to estimate the variances, which are second order derivatives of a distribution associated with the variables,
the determining of the order of the variables includes re-applying the same neural network, without retraining, to the dataset after each iterative removal of at least one node or variable to re-determine the variances,
each iterative removal of at least one node or variable is based on a score, and the scores for new distributions resulting from the iterative removals of at least one node or variable are determined based on the re-determined variances.
5 . The data processing apparatus according to claim 1 , wherein the processing circuity is configured to select parent variable(s) for each variable from preceding variable(s) in the order, wherein the selecting comprises an inference procedure and is followed by a pruning procedure to remove incorrect causal relationships.
6 . The data processing apparatus according to claim 1 , wherein the variances comprise variances of derivatives of a score in respect of each variable.
7 . The data processing apparatus according to claim 6 , wherein the score represents a gradient of a data distribution of the data set.
8 . The data processing apparatus according to claim 1 , wherein the variances comprise or are represented by a Jacobian or Hessian.
9 . The data processing apparatus according to claim 1 , wherein the processing circuitry is further configured to determine the variances based on a score, wherein the score is calculated by processing the at least one dataset by the model.
10 . The data processing apparatus according to claim 9 , wherein the score comprises, represents or is determined from gradients generated by processing the dataset by the model.
11 . The data processing apparatus according to claim 1 , wherein the order of the variables comprises or is represented by an order of nodes of a causal graph, for example a directed acyclic graph (DAG).
12 . The data processing apparatus according to claim 9 , wherein the processing circuitry is further configured to determine a leaf node that corresponds to a peripheral one of the variables based on the score.
13 . The data processing apparatus according to claim 12 , wherein the processing circuitry is further configured to determine an order subsequent to the leaf node by masking the leaf node and determining the variances without using variable(s) represented by the leaf node.
14 . The data processing apparatus according to claim 11 , wherein the processing circuity is configured to remove at least one node or variable represented by said at least one node, and to re-determine the variances thereby to determine the next node or variable in the order.
15 . The data processing apparatus according to claim 1 , wherein the processing circuitry is configured to perform an iterative procedure that comprises removing successive variable(s) or node(s) and re-determining variances to determine the next one(s) of the variable(s) or node(s) in the order.
16 . The data processing apparatus according to claim 15 , wherein the re-determining of variances is performed using the same trained model.
17 . The data processing apparatus according to claim 1 , wherein the model comprises at least one of a neural network, a generative model, a generative neural network, a diffusion model, a diffusion probabilistic model, a non-linear additive noise model.
18 . The data processing apparatus according to claim 1 , wherein the data set comprises data that includes or represents at least one of: drug dosages given to a patient or other subject; physiological or other measurements performed on the patient; one or more of blood pressure, temperature, heart rate, blood oxygenation, electrocardiograph or other electrical measurements; vision or hearing-related measurements; measurements of any of a patient's or other subject's senses or reactions or any other measurements; or at least one of age, height, weight or other patient data; data relating to an imaging or other procedure.
19 . A data processing method comprising:
storing a trained model;
receiving at least one dataset that comprises d variables and n samples;
determining variances associated with the variables by processing the dataset using the model; and
determining an order of the variables based on the determined variances including iteratively removing variables and/or nodes thereby to determine the order.