Evaluation of predictions as individual probability density functions
A system and method are disclosed to train machine learning models, generate predictions, and evaluate the predictions as individual probability density functions. Embodiments include a computer comprising a processor and memory and configured to train a first machine learning model to predict a mean demand of one or more items. Embodiments train a second machine learning model to predict a variance associated with the predicted mean demand. Embodiments use the first and second machine learning models and received current sales data to predict a negative binomial variance of demand of the one or more items, comprising a confidence interval specifying a stocking level for the one or more items that will satisfy a defined number of estimated outcomes. Embodiments generate an individual probability density function using the predicted mean demand of one or more items and the predicted negative binomial variance of demand, and evaluate the individual probability density function.
1 . A computer-implemented method, comprising:
training, by a computer comprising a processor and memory, a first machine learning model to predict a mean demand of one or more items, the one or more items stored at an inventory of one or more supply chain entities;
training, by the computer, a second machine learning model to predict a variance associated with the predicted mean demand of the one or more items, wherein the second machine learning model predicts the variance by minimizing a negative log-likelihood function;
receiving, by the computer, current sales data for the one or more items;
predicting, by the computer and using the trained first machine learning model, the trained second machine learning model, and the received current sales data, a negative binomial variance of demand of the one or more items, the negative binomial variance of demand comprising a confidence interval;
generating, by the computer, an individual probability density function, using the predicted mean demand of one or more items and the predicted negative binomial variance of demand as probability density function parameters of a distribution;
evaluating, by the computer, the generated individual probability density function;
initiating, by the computer, manufacturing of one or more components based, at least in part, on the predicted mean demand; and
setting, by the computer, inventory levels of the one or more items at one or more stocking points.
2 . The computer-implemented method of claim 1 , further comprising the computer evaluating the generated individual probability density function using one or more qualitative evaluation methods.
3 . The computer-implemented method of claim 1 , further comprising:
rendering, by the computer and for display on a user interface, a demand prediction feature explanation and evaluation visualization comprising the predicted mean demand of one or more items, the predicted negative binomial variance of demand, and the evaluated generated individual probability density function.
4 . The computer-implemented method of claim 1 , further comprising the computer evaluating the generated individual probability density function using one or more quantitative evaluation methods.
5 . The computer-implemented method of claim 2 , wherein at least one of the one or more qualitative evaluation methods comprises one or more methods selected from the list of:
cumulative distribution function histogram comparisons; and
inverse quantile plot comparisons.
6 . The computer-implemented method of claim 4 , wherein at least one of the one or more quantitative evaluation methods comprises:
generating, by the computer, a cumulative distribution function histogram of the generated individual probability density function; and
comparing, with the computer, the generated cumulative distribution function histogram of the generated individual probability density function to a uniform distribution.
7 . The computer-implemented method of claim 6 , wherein the computer compares the generated cumulative distribution function histogram of the generated individual probability density function to the uniform distribution using one or more of:
a Wasserstein metric; and
a Kullback-Leibler divergence.
8 . A system comprising a computer, the computer comprising a processor and memory and configured to:
train a first machine learning model to predict a mean demand of one or more items, the one or more items stored at an inventory of one or more supply chain entities;
train a second machine learning model to predict a variance associated with the predicted mean demand of the one or more items, wherein the second machine learning model predicts the variance by minimizing a negative log-likelihood function;
receive current sales data for the one or more items;
predict, using the trained first machine learning model, the trained second machine learning model, and the received current sales data, a negative binomial variance of demand of the one or more items, the negative binomial variance of demand comprising a confidence interval;
generate an individual probability density function, using the predicted mean demand of one or more items and the predicted negative binomial variance of demand as probability density function parameters of a distribution;
evaluate the generated individual probability density function;
initiate manufacturing of one or more components based, at least in part, on the predicted mean demand; and
set, by the computer, inventory levels of the one or more items at one or more stocking points.
9 . The system of claim 8 , further comprising the computer:
evaluating the generated individual probability density function using one or more qualitative evaluation methods.
10 . The system of claim 8 , further comprising the computer:
rendering, for display on a user interface, a demand prediction feature explanation and evaluation visualization comprising the predicted mean demand of one or more items, the predicted negative binomial variance of demand, and the evaluated generated individual probability density function.
11 . The system of claim 8 , further comprising the computer:
evaluating the generated individual probability density function using one or more quantitative evaluation methods.
12 . The system of claim 9 , wherein at least one of the one or more qualitative evaluation methods comprises one or more methods selected from the list of:
cumulative distribution function histogram comparisons; and
inverse quantile plot comparisons.
13 . The system of claim 11 , wherein at least one of the one or more quantitative evaluation methods comprises:
generating a cumulative distribution function histogram of the generated individual probability density function; and
comparing, the generated cumulative distribution function histogram of the generated individual probability density function to a uniform distribution.
14 . The system of claim 13 , wherein the computer compares the generated cumulative distribution function histogram of the generated individual probability density function to the uniform distribution using one or more of:
a Wasserstein metric; and
a Kullback-Leibler divergence.
15 . A non-transitory computer-readable storage medium embodied with software, the software when executed configured to:
train a first machine learning model to predict a mean demand of one or more items, the one or more items stored at an inventory of one or more supply chain entities;
train a second machine learning model to predict a variance associated with the predicted mean demand of the one or more items, wherein the second machine learning model predicts the variance by minimizing a negative log-likelihood function;
receive current sales data for the one or more items;
predict, using the trained first machine learning model, the trained second machine learning model, and the received current sales data, a negative binomial variance of demand of the one or more items, the negative binomial variance of demand comprising a confidence interval;
generate an individual probability density function, using the predicted mean demand of one or more items and the predicted negative binomial variance of demand as probability density function parameters of a distribution;
evaluate the generated individual probability density function;
initiate manufacturing of one or more components based, at least in part, on the predicted mean demand; and
set, by the computer, inventory levels of the one or more items at one or more stocking points.
16 . The non-transitory computer-readable storage medium of claim 15 , wherein the software when executed is further configured to:
evaluate the generated individual probability density function using one or more qualitative evaluation methods.
17 . The non-transitory computer-readable storage medium of claim 15 , wherein the software when executed is further configured to:
render, for display on a user interface, a demand prediction feature explanation and evaluation visualization comprising the predicted mean demand of one or more items, the predicted negative binomial variance of demand, and the evaluated generated individual probability density function.
18 . The non-transitory computer-readable storage medium of claim 15 , wherein the software when executed is further configured to:
evaluate the generated individual probability density function using one or more quantitative evaluation methods.
19 . The non-transitory computer-readable storage medium of claim 16 , wherein at least one of the one or more qualitative evaluation methods comprises one or more methods selected from the list of:
cumulative distribution function histogram comparisons; and
inverse quantile plot comparisons.
20 . The non-transitory computer-readable storage medium of claim 18 , wherein at least one of the one or more quantitative evaluation methods comprises:
generating a cumulative distribution function histogram of the generated individual probability density function; and
comparing, the generated cumulative distribution function histogram of the generated individual probability density function to a uniform distribution.