# US 2019/0244256 A1 · Systems and methods for response curve estimation for distribution of data elements on an electronic network > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 2019/0244256 A1 - Document ID: US20190244256A1 - Status: Published application - Kind: A1 - Application number: 16/384,548 - Filed: 2019-04-15 - Published: 2019-08-08 - Earliest claimed: 2013-05-13 - Assignees: Oath (Americas) Inc. - Applicants: Oath (Americas) Inc. - Inventors: Niklas KARLSSON - Web page: https://patentgrep.com/patent/US20190244256A1 ## CPC - G06Q 30/0275: {Auctions} - G06Q: INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR ## Abstract Systems, methods, and computer-readable media are disclosed for calculating input-output relationships using, for example, spline functions. In accordance with one implementation, a computer-implemented method is provided that includes determining at least one price-volume point comprising a price and associated volume, transforming the price, and using the transformed price to calculate values along a spline function to obtain a price-volume curve weight factor. The method further includes transforming a second price, calculating values along the spline function and the first derivative of the spline function using the transformed second price to obtain a volume estimate and volume rate at the second price, and recalculating the spline function based on the calculated price-volume curve weight factor, volume estimate, volume estimate and volume rate. ## Claims ### Claim at position 1 1-20. (canceled) ### Claim 21 A computer-implemented method of estimating response curves associated with the distribution of graphical data elements on an electronic network, the method comprising the following operations performed by one or more processors: determining at least one input-output point, comprising an input value and a corresponding output value, the input value and corresponding output value corresponding to the distribution of graphical data elements on the electronic network; transforming the input value of the at least one input-output point based on a range of input values; determining, based on the transformed at least one input value, values along a response curve to obtain a curve weight factor; transforming a second input value based on the range of valid input values; determining, based on the second transformed input value, values along the response curve and the first derivative of the response curve, to obtain an estimated output value and estimated output rate associated with the second input value; and redetermining the response curve based on the determined curve weight factor, estimated output value, and estimated output rate. ### Claim 22 (depends on 221) The method of claim 221, wherein the input value corresponds to an exchange bid and the output value corresponds to a volume associated with the exchange bid. ### Claim 23 (depends on 222) The method of claim 222, wherein the volume associated with the exchange bid represents a number of placements of graphical data elements on a network that placed the exchange bid at an exchange associated with the distribution of graphical data elements on the electronic network. ### Claim 24 (depends on 223) The method of claim 223, wherein the exchange associated with the distribution of graphical data elements on the electronic network comprises: receiving one or more exchange bids associated with one or more graphical data elements; determining the highest received exchange bid; and determining impression placements for graphical data elements associated with the highest exchange bid. ### Claim 25 (depends on 223) The method of claim 223, further comprising: determining one of a pacing or a delivery goal associated with distribution of the graphical data elements on the electronic network; determining a number of impressions needed to satisfy the determined goal; and determining, using the response curve, at least one exchange bid associated with the determined number of impressions. ### Claim 26 (depends on 221) The method of claim 221, wherein the response curve is non-decreasing and is constructed of more than one polynomial function. ### Claim 27 (depends on 221) The method of claim 221, wherein transforming an input value further comprises raising the input value to the power of a factor and determining the logarithm of an associated output value. ### Claim 28 A non-transitory computer-readable storage medium containing instructions for estimating response curves associated with the distribution of graphical data elements on an electronic network that, when executed by at least one electronic processor, causes the at least one electronic processor to perform the following operations: determining at least one input-output point, comprising an input value and a corresponding output value, the input value and corresponding output value corresponding to the distribution of graphical data elements on the electronic network; transforming the input value of the at least one input-output point based on a range of input values; determining, based on the transformed at least one input value, values along a response curve to obtain a curve weight factor; transforming a second input value based on the range of valid input values; determining, based on the second transformed input value, values along the response curve and the first derivative of the response curve, to obtain an estimated output value and estimated output rate associated with the second input value; and redetermining the response curve based on the determined curve weight factor, estimated output value, and estimated output rate. ### Claim 29 (depends on 28) The computer-readable medium of claim 28, wherein the input value corresponds to an exchange bid and the output value corresponds to a volume associated with the exchange bid. ### Claim 30 (depends on 29) The computer-readable medium of claim 29, wherein the volume associated with the exchange bid represents a number of placements of graphical data elements on a network that placed the exchange bid at an exchange associated with the distribution of graphical data elements on the electronic network. ### Claim 31 (depends on 30) The computer-readable medium of claim 30, wherein the exchange associated with the distribution of graphical data elements on the electronic network comprises: receiving one or more exchange bids associated with one or more graphical data elements; determining the highest received exchange bid; and determining impression placements for graphical data elements associated with the highest exchange bid. ### Claim 32 (depends on 30) The computer-readable medium of claim 30, further comprising: determining one of a pacing or a delivery goal associated with distribution of the graphical data elements on the electronic network; determining a number of impressions needed to satisfy the determined goal; and determining, using the response curve, at least one exchange bid associated with the determined number of impressions. ### Claim 33 (depends on 28) The computer-readable medium of claim 28, wherein the response curve is non-decreasing and is constructed of more than one polynomial function. ### Claim 34 (depends on 28) The computer-readable medium of claim 28, wherein transforming an input value further comprises raising the input value to the power of a factor and determining the logarithm of an associated output value. ### Claim 35 A system for estimating response curves, comprising: at least one electronic processor; and a storage device that stores instructions that, when executed by the at least one electronic processor, causes the at least one electronic processor to perform a method for estimating response curves associated with the distribution of graphical data elements on an electronic network comprising: determining at least one input-output point, comprising an input value and a corresponding output value, the input value and corresponding output value corresponding to the distribution of graphical data elements on the electronic network; transforming the input value of the at least one input-output point based on a range of input values; determining, based on the transformed at least one input value, values along a response curve to obtain a curve weight factor; transforming a second input value based on the range of valid input values; determining, based on the second transformed input value, values along the response curve and the first derivative of the response curve, to obtain an estimated output value and estimated output rate associated with the second input value; and redetermining the response curve based on the determined curve weight factor, estimated output value, and estimated output rate. ### Claim 36 (depends on 35) The system of claim 35, wherein the input value corresponds to an exchange bid and the output value corresponds to a volume associated with the exchange bid. ### Claim 37 (depends on 35) The system of claim 35, wherein the volume associated with the exchange bid represents a number of placements of graphical data elements on a network that placed the exchange bid at an exchange associated with the distribution of graphical data elements on the electronic network. ### Claim 38 (depends on 35) The system of claim 35, wherein the exchange associated with the distribution of graphical data elements on the electronic network comprises: receiving one or more exchange bids associated with one or more graphical data elements; determining the highest received exchange bid; and determining impression placements for graphical data elements associated with the highest exchange bid. ### Claim 39 (depends on 35) The system of claim 35, wherein the response curve is non-decreasing and is constructed of more than one polynomial function. ### Claim 40 (depends on 35) The system of claim 35, wherein transforming an input value further comprises raising the input value to the power of a factor and determining the logarithm of an associated output value.