A system, method and program product for providing cascade prediction. A system is disclosed having: a computing system for receiving observed cascade data, wherein the observed cascade data includes a set of nodes impacted prior to a preliminary time; a sub-cascade processing engine that determines a sub-cascade size of each node in the set of nodes; survival analysis system that utilizes a networked Weibull regression to determine a survival rate of each node in the set of nodes; and a calculation system that applies the survival rate to the sub-cascade size of each node in the set of nodes to generate a predicted cascade size at a future time.
Please help me write a proper abstract based on the patent claims. CLAIM: 1. A cascade prediction system, comprising: a computing system for receiving observed cascade data, wherein the observed cascade data includes a set of nodes impacted prior to a preliminary time; a sub-cascade processing engine that determines a sub-cascade size of each node in the set of nodes; survival analysis system that utilizes a networked Weibull regression to determine a survival rate of each node in the set of nodes; and a calculation system that applies the survival rate to the sub-cascade size of each node in the set of nodes to generate a predicted cascade size at a future time. 2. The cascade prediction system of claim 1, wherein the cascade prediction system utilizes node attributes to determine the sub-cascade size and survival rate for each node. 3. The cascade prediction system of claim 2, wherein the node attributes include an average inflow rate of followers of a user, an average republish rate of followers of the user, an inflow rate to the user, an outflow rate of the user, a number of followers to the user and a number of other users followed by the user. 4. The cascade prediction system of claim 1, wherein the observed cascade data comprises social media activity associated with a plurality of users republishing posts. 5. The cascade prediction system of claim 1, wherein the networked Weibull regression is an optimization problem that seeks to minimize the following: F  ( λ , k , β , γ ) = G 1  ( λ , k ) + μ   G 2  ( β , λ ) + η   G 3  ( γ , k ) G 1  ( λ , k ) = - log   L  ( λ , k ) G 2  ( λ , β ) = 1 2  N   log   λ - log   X · β  2 + α β   β  1 G 3  ( k , γ ) = 1 2  N   log   k - log   X · γ  2 + α γ   γ  1 where β and γ are r*1 regression coefficient vectors to λ and k, N is a number of users, L is a likelihood and X is a feature vector. 6. The cascade prediction system of claim 1, further comprising a response system that utilizes the predicted cascade size to alter a behavior of a network. 7. The cascade prediction system of claim 1, wherein the observed cascade data comprises information relating to a spread of a disease being tracked by a disease monitoring network. 8. A method for predicting cascades, comprising: providing a computing system for receiving observed cascade data, wherein the observed cascade data includes a set of nodes impacted prior to a preliminary time; determining a sub-cascade size of each node in the set of nodes; utilizing a networked Weibull regression to determine a survival rate of each node in the set of nodes; and applying the survival rate to the sub-cascade size of each node in the set of nodes to generate a predicted cascade size at a future time. 9. The method of claim 8, wherein node attributes are utilized to determine the sub-cascade size and survival rate for each node. 10. The method of claim 9, wherein the node attributes include an average inflow rate of followers of a user, an average republish rate of followers of the user, an inflow rate to the user, an outflow rate of the user, a number of followers to the user and a number of other users followed by the user. 11. The method of claim 8, wherein the observed cascade data comprises social media activity associated with a plurality of users republishing posts. 12. The method of claim 8, wherein the networked Weibull regression is an optimization problem that seeks to minimize the following: F  ( λ , k , β , γ ) = G 1  ( λ , k ) + μ   G 2  ( β , λ ) + η   G 3  ( γ , k ) G 1  ( λ , k ) = - log   L  ( λ , k ) G 2  ( λ , β ) = 1 2  N   log   λ - log   X · β  2 + α β   β  1 G 3  ( k , γ ) = 1 2  N   log   k - log   X · γ  2 + α γ   γ  1 where β and γ are r*1 regression coefficient vectors to λ and k, N is a number of users, L is a likelihood and X is a feature vector. 13. The method of claim 8, further comprising utilizing the predicted cascade size to alter a behavior of a network. 14. The method of claim 8, wherein the observed cascade data comprises information relating to a spread of a disease being tracked by a disease monitoring network. 15. A computer program product stored on a computer readable storage medium, which when executed by a processor, generates a cascade prediction, the computer program product comprising: programming instructions for receiving observed cascade data, wherein the observed cascade data includes a set of nodes impacted prior to a preliminary time; programming instructions for determining a sub-cascade size of each node in the set of nodes; and programming instructions for utilizing a networked Weibull regression to determine a survival rate of each node in the set of nodes; and programming instructions for applying the survival rate to the sub-cascade size of each node in the set of nodes to generate a predicted cascade size at a future time. 16. The computer program product of claim 15, wherein node attributes are utilized to determine the sub-cascade size and survival rate for each node. 17. The computer program product of claim 16, wherein the node attributes include an average inflow rate of followers to a user, an average republish rate of followers of the user, an inflow rate to the user, an outflow rate of the user, a number of followers of the user and a number of other users followed by the user. 18. The computer program product of claim 15, wherein the observed cascade data comprises one of social media activity associated with a plurality of users republishing posts and information relating to a spread of a disease being tracked by a disease monitoring network. 19. The computer program product of claim 15, wherein the networked Weibull regression is an optimization problem that seeks to minimize the following: F  ( λ , k , β , γ ) = G 1  ( λ , k ) + μ   G 2  ( β , λ ) + η   G 3  ( γ , k ) G 1  ( λ , k ) = - log   L  ( λ , k ) G 2  ( λ , β ) = 1 2  N   log   λ - log   X · β  2 + α β   β  1 G 3  ( k , γ ) = 1 2  N   log   k - log   X · γ  2 + α γ   γ  1 where β and γ are r*1 regression coefficient vectors to λ and k, N is a number of users, L is a likelihood and X is a feature vector. 20. The computer program product of claim 15, further comprising programming instructions for utilizing the predicted cascade size to alter a behavior of a network.