# US 2019/0318256 A1 · Method, apparatus and system for estimating causality among observed variables > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 2019/0318256 A1 - Document ID: US20190318256A1 - Status: Published application - Kind: A1 - Application number: 16/220,204 - Filed: 2018-12-14 - Published: 2019-10-17 - Earliest claimed: 2018-04-16 - Assignees: NEC Corporation - Applicants: NEC Corporation - Inventors: Wenjuan WEI; Chunchen LIU; Lu FENG - Web page: https://patentgrep.com/patent/US20190318256A1 ## CPC - G06N 5/046: Forward inferencing; Production systems - G06N 20/00: Machine learning - G06F 16/313: {Selection or weighting of terms for indexing} - G06F 16/9024: {Graphs; Linked lists (G06F16/9027 takes precedence)} - G06N 5/013: {Automatic theorem proving} - G06N 5/022: Knowledge engineering; Knowledge acquisition - G06N 7/01: Probabilistic graphical models, e.g. probabilistic networks - G06N: COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS - G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N) ## Abstract In response to receiving observed data of mixed observed variables, a mixed causality objective function, being suitable for continuous observed variables and discrete observed variables is determined, wherein the mixed causality objective function includes a causality objective function for continuous observed variables and a causality objective function for discrete observed variables and the fitting inconsistency is adjusted based on weighted factors of the observed variables. Then, the mixed causality objective function is optimally solved by using a mixed sparse causal inference, suitable for both continuous observed variables and discrete observed variables, using the mixed observed data under a constraint of a directed acyclic graph, to estimate causality among the observed variables. ## Claims ### Claim 1 A method for estimating causality among observed variables, comprising: in response to receiving observed data of mixed observed variables, determining a mixed causality objective function suitable for continuous observed variables and discrete observed variables, based on fitting inconsistency upon fitting with the observed variables and sparsity constraints on a causal network structure for the observed variables, wherein the mixed causality objective function includes a causality objective function for continuous observed variables and a causality objective function for discrete observed variables, wherein the fitting inconsistency is adjusted based on weighted factors of the observed variables, a weighted factor of an observed variable represents a lower limit of a minimum cost required for fitting an object variable using other observed variables than the observed variable, and weighted factors for the discrete observed variables are different from weighted factors for the continuous observed variables; and optimally solving a mixed causality objective function for the observed variables by means of a mixed sparse causal inference, which is suitable for both continuous observed variables and discrete observed variables, using the observed data under a constraint of directed acyclic graph, to estimate causality among the observed variables. ### Claim 2 (depends on 1) The method of claim 1, wherein a causality objective function for continuous observed variables is built on an assumption that errors of observed variables comply with a Laplace distributions and a causality objective function for discrete observed variables is built on an assumption that errors of observed variables comply with a logistic distribution. ### Claim 3 (depends on 1) The method of claim 1, wherein the weighted factors for continuous observed variables are calculated on an assumption that errors of observed variables comply with a Laplace distribution and the weighted factors for discrete observed variables are calculated on an assumption that errors of observed variables comply with a logistic distribution. ### Claim 4 (depends on 1) The method of claim 1, wherein the mixed sparse causal inference for the mixed causality objective function for the observed variables is converted into a problem of solving an optimal causal sequence with recursion, wherein a cost from a starting node to a current node and a predicted cost from a current node to a target node in a sorted causal sequence are determined based on fitting inconsistency adjusted by the weighted factors of the observed variables and sparsity constraints on a causal network structure for the observed variables. ### Claim 5 (depends on 1) The method of claim 1, wherein the sparsity constraint is L0 sparsity constraint. ### Claim 6 (depends on 5) The method of claim 5, further comprising, in a process of solving an optimal causal sequence recursion: determining, for a newly generated candidate causal sequence, whether it is in conflict with a predetermined sequential relation of variable groups; and if it is determined that there is a conflict, abandoning the newly generated candidate causal sequence. ### Claim 7 (depends on 6) The method of claim 6, wherein the predetermined sequential relation of variable groups is determined based on one or more of following ways: being given by experts in the field; or being automatically determined based on the observed data. ### Claim 8 (depends on 7) The method of claim 7, wherein the predetermined sequential relation of variable groups is automatically determined based on the observed data by: obtaining a potentially optimal parent node set for each of the observed variables; generating a parent relation graph based on the obtained optimal parent node set; extracting strongly connected components from the parent relation graph; converting the parent relation graph into a new directed acyclic graph by converting each component in the strongly connected components into a new node and adding a corresponding edge between respective new nodes in the presence of connectivity between two strongly connected components in the parent relation graph; and extracting a sequential relation between strongly connected components in the directed acyclic graph as the predetermined sequential relation of variable groups. ### Claim 9 An apparatus for estimating causality among observed variables, comprising: a mixed objective function determination module configured to, in response to receiving observed data of mixed observed variables, determine a mixed causality objective function suitable for continuous observed variables and discrete observed variables, based on fitting inconsistency upon fitting with the observed variables and sparsity constraints on a causal network structure for the observed variables, wherein the mixed causality objective function includes a causality objective function for continuous observed variables and a causality objective function for discrete observed variables, wherein the fitting inconsistency is adjusted based on weighted factors of the observed variables, a weighted factor of an observed variables represents a lower limit of a minimum cost required for fitting an object variable using other observed variables than the observed variable, and weighted factors for the discrete observed variables are different from weighted factors for the continuous observed variables; and a mixed causal inference module configured to optimally solve a mixed causality objective function for the observed variables by means of a mixed sparse causal inference, which is suitable for both continuous observed variables and discrete observed variables, using the observed data under a constraint of directed acyclic graph, to estimate causality among the observed variables. ### Claim 10 (depends on 9) The apparatus of claim 9, wherein a causality objective function for continuous observed variables is built on an assumption that errors of observed variables comply with a Laplace distribution and a causality objective function for discrete observed variables is built on an assumption that errors of observed variables comply with a logistic distribution. ### Claim 11 (depends on 9) The apparatus of claim 9, wherein the weighted factors for continuous observed variables are calculated on an assumption that errors of observed variables comply with a Laplace distribution and the weighted factors for discrete observed variables are calculated on an assumption that errors of observed variables comply with a logistic distribution. ### Claim 12 (depends on 9) The apparatus of claim 9, wherein the mixed causal inference module is configured to convert the mixed sparse causal inference for the mixed causality objective function for the observed variables into a problem of solving an optimal causal sequence with recursion, wherein the causal inference module is configured to determine, based on fitting inconsistency adjusted by the weighted factor of the observed variables and sparsity constraints on a causal network structure for the observed variables, a cost from a starting node to a current node and a predicted cost from a current node to a target node in a sorted causal sequence. ### Claim 13 (depends on 9) The apparatus of claim 9, wherein the sparsity constraint is L0 sparsity constraint. ### Claim 14 (depends on 13) The apparatus of claim 13, further comprising a search space pruning module configured to, in a process of solving the optimal causal sequence recursion: determine, for a newly generated candidate causal sequence, whether it is in conflict with a predetermined sequential relation of variable groups; and if it is determined that there is a conflict, abandon the newly generated candidate causal sequence. ### Claim 15 (depends on 14) The apparatus of claim 14, wherein the predetermined sequential relation of variable groups is determined based on one or more of following ways: being given by experts in the field; or being automatically determined based on the observed data. ### Claim 16 (depends on 15) The apparatus of claim 15, further comprising a sequential relation determination module configured to automatically determine the predetermined sequential relation of variable groups by: obtaining a potentially optimal parent node set for each of the observed variables; generating a parent relation graph based on the obtained optimal parent node set; extracting strongly connected components from the parent relation graph; converting the parent relation graph into a new directed acyclic graph by converting each component in the strongly connected components into a new node and adding a corresponding edge between respective new nodes in the presence of connectivity between two strongly connected components in the parent relation graph; and extracting a sequential relation between strongly connected components in the directed acyclic graph as the predetermined sequential relation of variable groups. ### Claim 17 (depends on 1) A system for estimating causality among observed variables, comprising: a processor; and a memory having computer program codes stored therein which, when executed by the processor, causing the processing to perform the method according to claim 1. ### Claim 18 (depends on 1) A computer-readable storage medium having computer program codes stored thereon, the computer program codes, when executed by a processor, performing the method according to claim 1.