Image discrimination has become an essential task in the era of artificial intelligence, with convolutional neural networks frequently delivering high predictive accuracy. Influential patterns within images can manifest in either fixed or random locations. While generalized linear model-based approaches have shown effectiveness for scenarios involving fixed-location influential patterns, literature on methodologies addressing random locations remains scarce in statistical research. To address this gap, we propose a novel model that assigns a positive label to an image if at least one of its sub-images contains a specific pattern and a negative label if none are present. This multiple-instance logistic regression framework effectively models the detection of randomly located patterns using a parsimonious approach, in contrast to convolutional neural networks, which typically require extensive parameterization. We apply our proposed convolutional multiple-instance logistic regression model to various datasets, including Malaria, Poker, Brain MRI, and MNIST, illustrating the trade-off between model explainability and predictive accuracy.