We establish a broad methodological foundation for mixed-integer optimization with learned constraints. We propose an end-to-end pipeline for data-driven decision making in which constraints and objectives are directly learned from data using machine learning, and the trained models are embedded in an optimization formulation. We exploit the mixed-integer optimization-representability of many machine learning methods, including linear models, decision trees, ensembles, and multi-layer perceptrons. The consideration of multiple methods allows us to capture various underlying relationships between decisions, contextual variables, and outcomes. We also characterize a decision trust region using the convex hull of the observations, to ensure credible recommendations and avoid extrapolation. We efficiently incorporate this representation using column generation and clustering. In combination with domain-driven constraints and objective terms, the embedded models and trust region define a mixed-integer optimization problem for prescription generation. We implement this framework as a Python package (OptiCL) for practitioners. We demonstrate the method in both chemotherapy optimization and World Food Programme planning. The case studies illustrate the benefit of the framework in generating high-quality prescriptions, the value added by the trust region, the incorporation of multiple machine learning methods, and the inclusion of multiple learned constraints.

Random forests have been widely used for their ability to provide so-called importance measures, which give insight at a global (per dataset) level on the relevance of input variables to predict a certain output. On the other hand, methods based on Shapley values have been introduced to refine the analysis of feature relevance in tree-based models to a local (per instance) level. In this context, we first show that the global Mean Decrease of Impurity (MDI) variable importance scores correspond to Shapley values under some conditions. Then, we derive a local MDI importance measure of variable relevance, which has a very natural connection with the global MDI measure and can be related to a new notion of local feature relevance. We further link local MDI importances with Shapley values and discuss them in the light of related measures from the literature. The measures are illustrated through experiments on several classification and regression problems.

Decision trees represent a connecting series of tests that branch off further and further down until a specific path matches a class or label. They're kind of like a flowing chart of coin flips, if/else statements, or conditions that when met lead to an end result. Decision trees are incredibly useful for classification problems in machine learning because it allows data scientists to choose specific parameters to define their classifiers. So whether you're presented with a price cutoff or target KPI value for your data, you have the ability to sort data at multiple levels and create accurate prediction models. Now there are many, many applications that utilize decision trees but for this article, I'm going to focus on using decision trees to make business decisions.

Importance: Lower-resource areas in Africa and Asia face a unique set of healthcare challenges: the dual high burden of communicable and non-communicable diseases; a paucity of highly trained primary healthcare providers in both rural and densely populated urban areas; and a lack of reliable, inexpensive internet connections. Objective: To address these challenges, we designed an artificial intelligence assistant to help primary healthcare providers in lower-resource areas document demographic and medical sign/symptom data and to record and share diagnostic data in real-time with a centralized database. Design: We trained our system using multiple data sets, including US-based electronic medical records (EMRs) and open-source medical literature and developed an adaptive, general medical assistant system based on machine learning algorithms. Main outcomes and Measure: The application collects basic information from patients and provides primary care providers with diagnoses and prescriptions suggestions. The application is unique from existing systems in that it covers a wide range of common diseases, signs, and medication typical in lower-resource countries; the application works with or without an active internet connection. Results: We have built and implemented an adaptive learning system that assists trained primary care professionals by means of an Android smartphone application, which interacts with a central database and collects real-time data. The application has been tested by dozens of primary care providers. Conclusions and Relevance: Our application would provide primary healthcare providers in lower-resource areas with a tool that enables faster and more accurate documentation of medical encounters. This application could be leveraged to automatically populate local or national EMR systems.

Linear temporal logic (LTL) is a specification language for finite sequences (called traces) widely used in program verification, motion planning in robotics, process mining, and many other areas. We consider the problem of learning LTL formulas for classifying traces; despite a growing interest of the research community, existing solutions suffer from two limitations: they do not scale beyond small formulas, and they may exhaust computational resources without returning any result. We introduce a new algorithm addressing both issues: our algorithm is able to construct formulas an order of magnitude larger than previous methods, and it is anytime, meaning that it in most cases successfully outputs a formula, albeit possibly not of minimal size. We evaluate the performances of our algorithm using an open source implementation against publicly available benchmarks.

Recently, there has been a growing interest in creating synergies between Combinatorial Optimization (CO) and Machine Learning (ML), and vice-versa. This is a natural connection since ML algorithms can be seen in essence as optimization algorithms that try to minimize prediction error. In this paper, we focus on how CO techniques can be applied to improve decision tree classifiers in ML. A decision tree classifier is a supervised ML technique that builds a tree-structured classifier, where internal nodes represent the features of a dataset, branches represent the decision rules and each leaf node represents the outcome. In essence, every path from the root to a leaf is a classification rule that determines to which class belongs the input query.

Isolation forest or "iForest" is an intuitive and widely used algorithm for anomaly detection that follows a simple yet effective idea: in a given data distribution, if a threshold (split point) is selected uniformly at random within the range of some variable and data points are divided according to whether they are greater or smaller than this threshold, outlier points are more likely to end up alone or in the smaller partition. The original procedure suggested the choice of variable to split and split point within a variable to be done uniformly at random at each step, but this paper shows that "clustered" diverse outliers - oftentimes a more interesting class of outliers than others - can be more easily identified by applying a non-uniformly-random choice of variables and/or thresholds. Different split guiding criteria are compared and some are found to result in significantly better outlier discrimination for certain classes of outliers.

Welcome to my new article series: Boosting algorithms in machine learning! This is Part 1 of the series. Here, I'll give you a short introduction to boosting, its objective, some key definitions and a list of boosting algorithms that we intend to cover in the next posts. You should be familiar with elementary tree-based machine learning models such as decision trees and random forests. In addition to that, it is recommended to have good knowledge of Python and its Scikit-learn library.

The efficacy of machine learning models is typically determined by computing their accuracy on test data sets. However, this may often be misleading, since the test data may not be representative of the problem that is being studied. With QuantifyML we aim to precisely quantify the extent to which machine learning models have learned and generalized from the given data. Given a trained model, QuantifyML translates it into a C program and feeds it to the CBMC model checker to produce a formula in Conjunctive Normal Form (CNF). The formula is analyzed with off-the-shelf model counters to obtain precise counts with respect to different model behavior. QuantifyML enables i) evaluating learnability by comparing the counts for the outputs to ground truth, expressed as logical predicates, ii) comparing the performance of models built with different machine learning algorithms (decision-trees vs. neural networks), and iii) quantifying the safety and robustness of models.

Loop closure detection is an essential tool of Simultaneous Localization and Mapping (SLAM) to minimize drift in its localization. Many state-of-the-art loop closure detection (LCD) algorithms use visual Bag-of-Words (vBoW), which is robust against partial occlusions in a scene but cannot perceive the semantics or spatial relationships between feature points. CNN object extraction can address those issues, by providing semantic labels and spatial relationships between objects in a scene. Previous work has mainly focused on replacing vBoW with CNN-derived features. In this paper, we propose SymbioLCD, a novel ensemble-based LCD that utilizes both CNN-extracted objects and vBoW features for LCD candidate prediction. When used in tandem, the added elements of object semantics and spatial-awareness create a more robust and symbiotic loop closure detection system. The proposed SymbioLCD uses scale-invariant spatial and semantic matching, Hausdorff distance with temporal constraints, and a Random Forest that utilizes combined information from both CNN-extracted objects and vBoW features for predicting accurate loop closure candidates. Evaluation of the proposed method shows it outperforms other Machine Learning (ML) algorithms - such as SVM, Decision Tree and Neural Network, and demonstrates that there is a strong symbiosis between CNN-extracted object information and vBoW features which assists accurate LCD candidate prediction. Furthermore, it is able to perceive loop closure candidates earlier than state-of-the-art SLAM algorithms, utilizing added spatial and semantic information from CNN-extracted objects.