The widespread adoption of deep learning is often attributed to its automatic feature construction with minimal inductive bias. However, in many real-world tasks, the learned function is intended to satisfy domain-specific constraints. We focus on monotonicity constraints, which are common and require that the function's output increases with increasing values of specific input features. We develop a counterexample-guided technique to provably enforce monotonicity constraints at prediction time. Additionally, we propose a technique to use monotonicity as an inductive bias for deep learning. It works by iteratively incorporating monotonicity counterexamples in the learning process. Contrary to prior work in monotonic learning, we target general ReLU neural networks and do not further restrict the hypothesis space. We have implemented these techniques in a tool called COMET. Experiments on real-world datasets demonstrate that our approach achieves state-of-the-art results compared to existing monotonic learners, and can improve the model quality compared to those that were trained without taking monotonicity constraints into account.

This provides a new general approach for learning monotonic neural networks with arbitrary model structures.

In many machine learning tasks, it is often necessary for the relationship between input and output variables to be monotonic, including both strictly monotonic and implicitly monotonic relationships. Traditional methods for maintaining monotonicity mainly rely on construction or regularization techniques, whereas this paper shows that the issue of strict monotonic probability can be viewed as a partial order between an observable revenue variable and a latent cost variable. This perspective enables us to reformulate the monotonicity challenge into modeling the latent cost variable. To tackle this, we introduce a generative network for the latent cost variable, termed the Generative Cost Model (GCM), which inherently addresses the strict monotonic problem, and propose the Implicit Generative Cost Model (IGCM) to address the implicit monotonic problem. We further validate our approach with a numerical simulation of quantile regression and conduct multiple experiments on public datasets, showing that our method significantly outperforms existing monotonic modeling techniques. The code for our experiments can be found at https://github.com/tyxaaron/GCM.

This provides a new general approach for learning monotonic neural networks with arbitrary model structures.

Summary and Contributions: RE authors' feedback: I think this method is primarily useful for offline evaluation with no latency requirements. There are many such use cases justifying the relevance of this work. However, I think the authors should be clear and upfront about the scalability and latency issues with their proposed methods and mention that in the paper. The previous submission of this work that I reviewed did no have any timing details, and I'm happy the added that to the experimental section. My overall score remains the same.

The reviewers agreed that this was an interesting and novel approach to imposing monotonicity, and that the paper was mostly well-written (although R4's review contains some suggested improvements). The main criticisms were that (i) the datasets in the experiments were small, and (ii) using an SMT solver at evaluation time might be too expensive for many applications. R3 also mentioned that the limitation to ReLU networks could be somewhat constraining. These issues, however, were agreed to be outweighed by the strengths of the paper, and all reviewers recommended acceptance. Please carefully read the reviews, and take them seriously when making edits: the paper is very good already, and while of course experiments should not be overhauled between submission and a final version, implementing some of the reviewers' suggestions (especially adding a more in-depth discussion of evaluation-time costs, and their impact on real-world systems) could improve it even further.

The widespread adoption of deep learning is often attributed to its automatic feature construction with minimal inductive bias. However, in many real-world tasks, the learned function is intended to satisfy domain-specific constraints. We focus on monotonicity constraints, which are common and require that the function's output increases with increasing values of specific input features. We develop a counterexample-guided technique to provably enforce monotonicity constraints at prediction time. Additionally, we propose a technique to use monotonicity as an inductive bias for deep learning.

Temporal Point Processes (TPPs) hold a pivotal role in modeling event sequences across diverse domains, including social networking and e-commerce, and have significantly contributed to the advancement of recommendation systems and information retrieval strategies. Through the analysis of events such as user interactions and transactions, TPPs offer valuable insights into behavioral patterns, facilitating the prediction of future trends. However, accurately forecasting future events remains a formidable challenge due to the intricate nature of these patterns. The integration of Neural Networks with TPPs has ushered in the development of advanced deep TPP models. While these models excel at processing complex and nonlinear temporal data, they encounter limitations in modeling intensity functions, grapple with computational complexities in integral computations, and struggle to capture long-range temporal dependencies effectively. In this study, we introduce the CuFun model, representing a novel approach to TPPs that revolves around the Cumulative Distribution Function (CDF). CuFun stands out by uniquely employing a monotonic neural network for CDF representation, utilizing past events as a scaling factor. This innovation significantly bolsters the model's adaptability and precision across a wide range of data scenarios. Our approach addresses several critical issues inherent in traditional TPP modeling: it simplifies log-likelihood calculations, extends applicability beyond predefined density function forms, and adeptly captures long-range temporal patterns. Our contributions encompass the introduction of a pioneering CDF-based TPP model, the development of a methodology for incorporating past event information into future event prediction, and empirical validation of CuFun's effectiveness through extensive experimentation on synthetic and real-world datasets.

Deep learning based image quality assessment (IQA) models usually learn to predict image quality from a single dataset, leading the model to overfit specific scenes. To account for this, mixed datasets training can be an effective way to enhance the generalization capability of the model. However, it is nontrivial to combine different IQA datasets, as their quality evaluation criteria, score ranges, view conditions, as well as subjects are usually not shared during the image quality annotation. In this paper, instead of aligning the annotations, we propose a monotonic neural network for IQA model learning with different datasets combined. In particular, our model consists of a dataset-shared quality regressor and several dataset-specific quality transformers. The quality regressor aims to obtain the perceptual qualities of each dataset while each quality transformer maps the perceptual qualities to the corresponding dataset annotations with their monotonicity maintained. The experimental results verify the effectiveness of the proposed learning strategy and our code is available at https://github.com/fzp0424/MonotonicIQA.

We propose a novel method, termed SuMo-net, that uses partially monotonic neural networks to learn a time-to-event distribution from a sample of covariates and right-censored times. SuMo-net models the survival function and the density jointly, and optimizes the likelihood for right-censored data instead of the often used partial likelihood. The method does not make assumptions about the true survival distribution and avoids computationally expensive integration of the hazard function. We evaluate the performance of the method on a range of datasets and find competitive performance across different metrics and improved computational time of making new predictions.