# US 2019/0377771 A1 · System and method of pre-processing discrete datasets for use in machine learning > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 2019/0377771 A1 - Document ID: US20190377771A1 - Status: Published application - Kind: A1 - Application number: 16/272,442 - Filed: 2019-02-11 - Published: 2019-12-12 - Earliest claimed: 2018-06-11 - Inventors: Andre J. UNGER; Robert William ENOUY - Web page: https://patentgrep.com/patent/US20190377771A1 ## CPC - G06F 17/14: Fourier, Walsh or analogous domain transformations {, e.g. Laplace, Hilbert, Karhunen-Loeve, transforms (for correlation function computation G06F17/156; spectrum analysers G01R23/16)} - G06F 17/18: for evaluating statistical data {, e.g. average values, frequency distributions, probability functions, regression analysis (forecasting specially adapted for a specific administrative, business or logistic context G06Q10/04)} - G06N 7/01: Probabilistic graphical models, e.g. probabilistic networks - G06N 20/00: Machine learning - G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N) - G06N: COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS ## Abstract There is provided a system and method of pre-processing discrete datasets for use in machine learning. The method includes: determining a median and a standard deviation of an input discrete dataset; determining a probability mass function including a probability of finding a particular data point in the input discrete dataset within a particular bin of a histogram representative of the input discrete dataset; transforming the probability mass function into a continuously differentiable probability density function using the standard deviation, the probability density function determined using a parametric control function, the parametric control function including a lognormal derivative of the probability density function, the parameters within the control function are estimated using optimization that minimizes a mean-squared error of an objective function; and outputting the probability density function for use an input to a machine learning model. ## Claims ### Claim 1 A method of pre-processing discrete datasets for use in machine learning, the method executable on one or more computer processors, the method comprising: receiving an input discrete dataset; determining a median and a standard deviation of the input discrete dataset; generating a probability mass function comprising a probability of finding a particular data point in the input discrete dataset within a particular bin of a histogram representative of the input discrete dataset; transforming the probability mass function into a continuously differentiable probability density function using the standard deviation, the probability density function determined using a parametric control function, the parametric control function comprising a lognormal derivative of the probability density function, the parameters within the control function are estimated using optimization that minimizes a mean-squared error of an objective function; and outputting the probability density function for use an input to a machine learning model. ### Claim 2 (depends on 1) The method of claim 1, further comprising discarding any data point greater than a predetermined culling threshold. ### Claim 3 (depends on 1) The method of claim 1, wherein the input discrete dataset comprising a unimodal distribution and the parametric control function comprising a linear function. ### Claim 4 (depends on 3) The method of claim 3, wherein the parametric control function further comprising at least one of polynomial terms and Fourier terms. ### Claim 5 (depends on 1) The method of claim 1, wherein the input discrete dataset comprising a multi-modal distribution and the parametric control function comprising a parameterized modified Fourier series. ### Claim 6 (depends on 1) The method of claim 1, further comprising: transforming the input discrete dataset into a median relative space; determining a cumulative mass function as a summation over bins of the probability mass function; mapping the cumulative mass function to the median relative space; determining a cumulative distribution function as an integration of the probability density function; and mapping the cumulative distribution function into the median-relative space, wherein the minimizing mean-squared error of the objective function comprising minimizing the difference between the cumulative distribution function and the cumulative mass function in the median-relative space. ### Claim 7 (depends on 6) The method of claim 6, wherein the transforming of the input discrete dataset into the median relative space comprising a linear transformation. ### Claim 8 (depends on 6) The method of claim 6, wherein the transforming of the input discrete dataset into the median relative space comprising a lognormal transformation. ### Claim 9 (depends on 6) The method of claim 6, further comprising determining a goodness of fit of the parametric probability density function comprising minimizing a mean-squared error between an arithmetic mean of the input discrete dataset in the median-relative space and a mean of the probability density function in the median-relative space. ### Claim 10 (depends on 6) The method of claim 6, further comprising adding additional polynomial terms to the objective function incrementally until the mean-squared error between the cumulative distribution function and the cumulative mass function in the median-relative space is minimized. ### Claim 11 A system of pre-processing discrete datasets for use in machine learning, the system comprising one or more processors and one or more non-transitory computer storage media, the one or more non-transitory computer storage media causing the one or more processors to execute: an input module to receive an input discrete dataset; a compression module to: determine a median and a standard deviation of the input discrete dataset; determine a probability mass function comprising a probability of finding a particular data point in the input discrete dataset within a particular bin of a histogram representative of the input discrete dataset; and transform the probability mass function into a continuously differentiable probability density function using the standard deviation, the probability density function determined using a parametric control function, transforming the probability mass function into a continuously differentiable probability density function using the standard deviation, the probability density function determined using a parametric control function, the parametric control function comprising a lognormal derivative of the probability density function, the parameters within the control function are estimated using optimization that minimizes a mean-squared error of an objective function, the parameters within the control function are estimated using optimization that minimizes a mean-squared error; and an output module to output the probability density function for use an input to a machine learning model. ### Claim 12 (depends on 11) The system of claim 11, the compression module further discarding any data point greater than a predetermined culling threshold. ### Claim 13 (depends on 11) The system of claim 11, wherein the input discrete dataset comprising a unimodal distribution and the parametric control function comprising a linear function. ### Claim 14 (depends on 13) The system of claim 13, wherein the parametric control function further comprising at least one of polynomial terms and Fourier terms. ### Claim 15 (depends on 11) The system of claim 11, wherein the input discrete dataset comprising a multi-modal distribution and the parametric control function comprising a parameterized modified Fourier series. ### Claim 16 (depends on 11) The system of claim 11, the compression module further: transforming the input discrete dataset into a median relative space; determining a cumulative mass function as a summation over bins of the probability mass function; mapping the cumulative mass function to the median relative space; determining a cumulative distribution function as an integration of the probability density function; and mapping the cumulative distribution function into the median-relative space, wherein minimizing the mean-squared error of the objective function comprising minimizing the difference between the cumulative distribution function and the cumulative mass function in the median-relative space. ### Claim 17 (depends on 16) The system of claim 16, wherein the transforming of the input discrete dataset into the median relative space comprising a linear transformation. ### Claim 18 (depends on 16) The system of claim 16, wherein the transforming of the input discrete dataset into the median relative space comprising a lognormal transformation. ### Claim 19 (depends on 16) The system of claim 16, the compression module further determining a goodness of fit of the parametric probability density function comprising minimizing a mean-squared error between an arithmetic mean of the input discrete dataset in the median-relative space and a mean of the probability density function in the median-relative space. ### Claim 20 (depends on 16) The system of claim 16, the compression module further adding additional polynomial terms to the objective function incrementally until the mean-squared error between the cumulative distribution function and the cumulative mass function in the median-relative space is minimized.