Personalized marketing in retail requires a model to predict how different marketing actions affect product choices by individual customers. Large retailers often handle millions of transactions daily, involving thousands of products in hundreds of categories. Product choice models thus need to scale to large product assortments and customer bases, without extensive product attribute information. To address these challenges, we propose a custom deep neural network model. The model incorporates bottleneck layers to encode cross-product relationships, calibrates time-series filters to capture purchase dynamics for products with different interpurchase times, and relies on weight sharing between the products to improve convergence and scale to large assortments. The model applies to loyalty card transaction data without predefined categories or product attributes to predict customer-specific purchase probabilities in response to marketing actions. In a simulation, the proposed product choice model predicts purchase decisions better than baseline methods by adjusting the predicted probabilities for the effects of recent purchases and price discounts. The improved predictions lead to substantially higher revenue gains in a simulated coupon personalization problem. We verify predictive performance using transaction data from a large retailer with experimental variation in price discounts.