Surrogate Modeling via Factorization Machine and Ising Model with Enhanced Higher-Order Interaction Learning

TL;DR

An enhanced surrogate model is proposed that incorporates additional slack variables into both the factorization machine and its associated Ising representation thereby unifying what was by design a two-step process into a single, integrated step, offering a promising approach for building efficient surrogate models that exploit potential quantum advantages.

Abstract

Recently, a surrogate model was proposed that employs a factorization machine to approximate the underlying input-output mapping of the original system, with quantum annealing used to optimize the resulting surrogate function. Inspired by this approach, we propose an enhanced surrogate model that incorporates additional slack variables into both the factorization machine and its associated Ising representation thereby unifying what was by design a two-step process into a single, integrated step. During the training phase, the slack variables are iteratively updated, enabling the model to account for higher-order feature interactions. We apply the proposed method to the task of predicting drug combination effects. Experimental results indicate that the introduction of slack variables leads to a notable improvement of performance. Our algorithm offers a promising approach for building efficient surrogate models that exploit potential quantum advantages.

Figures (6)

• Figure 1: Schematic diagram illustrating the training and test data split. Training data are marked by circles, and test data by crosses. (a) Prediction of dose-response matrix for a given drug combination. In this scenario, we select three types of data points as training samples: single-drug responses (shown in blue), diagonal combinations (green), and a set of randomly selected combination-dose pairs (magenta). The goal is to predict the full dose-response matrix based on these sparse observations. (b) Prediction of unseen drug combination effects. Here, the dataset is first divided into tested drug combinations and unseen drug combinations. For the tested combinations, the data are further split into training and test sets following the same approach as in panel (a). For the unseen combinations, however, no drug combination data are available during training—Only the test single-drug samples (crosses) are known.
• Figure 2: Correlations in the first prediction scenario, which focuses on reconstructing the dose-response matrix for a given drug combination. Each matrix is trained independently, and the reported correlations are averaged over all $192$ drug combinations.
• Figure 3: Correlations in the second scenario on prediction of unseen drug combination effect for a certain cell line. The correlations are the average of ten cell lines.
• Figure 4: Comparison between the true responses and the predicted responses. (a) No slack variable. (b) Sixteen slack variables.
• Figure 5: Comparison between the true responses and the predicted responses with only the best responses of all the dose-response matrices are shown. (a) No slack variable. (b) Sixteen slack variables.