Factor analysis or sometimes referred to as variable analysis has been extensively used in classification problems for identifying specific factors that are significant to particular classes. This type of analysis has been widely used in application such as customer segmentation, medical research, network traffic, image, and video classification. Today, factor analysis is prominently being used in fault diagnosis of machines to identify the significant factors and to study the root cause of a specific machine fault. The advantage of performing factor analysis in machine maintenance is to perform prescriptive analysis (helps answer what actions to take?) and preemptive analysis (helps answer how to eliminate the failure mode?). In this paper, a real case of an industrial rotating machine was considered where vibration and ambient temperature data was collected for monitoring the health of the machine. Gaussian mixture model-based clustering was used to cluster the data into significant groups, and spectrum analysis was used to diagnose each cluster to a specific state of the machine. The significant features that attribute to a particular mode of the machine were identified by using the random forest classification model. The significant features for specific modes of the machine were used to conclude that the clusters generated are distinct and have a unique set of significant features.

Methods for interpreting machine learning black-box models increase the outcomes' transparency and in turn generates insight into the reliability and fairness of the algorithms. However, the interpretations themselves could contain significant uncertainty that undermines the trust in the outcomes and raises concern about the model's reliability. Focusing on the method "Local Interpretable Model-agnostic Explanations" (LIME), we demonstrate the presence of two sources of uncertainty, namely the randomness in its sampling procedure and the variation of interpretation quality across different input data points. Such uncertainty is present even in models with high training and test accuracy. We apply LIME to synthetic data and two public data sets, text classification in 20 Newsgroup and recidivism risk-scoring in COMPAS, to support our argument.

Decision tree algorithms have been among the most popular algorithms for interpretable (transparent) machine learning since the early 1980's. The problem that has plagued decision tree algorithms since their inception is their lack of optimality, or lack of guarantees of closeness to optimality: decision tree algorithms are often greedy or myopic, and sometimes produce unquestionably suboptimal models. Hardness of decision tree optimization is both a theoretical and practical obstacle, and even careful mathematical programming approaches have not been able to solve these problems efficiently. This work introduces the first practical algorithm for optimal decision trees for binary variables. The algorithm is a co-design of analytical bounds that reduce the search space and modern systems techniques, including data structures and a custom bit-vector library. We highlight possible steps to improving the scalability and speed of future generations of this algorithm based on insights from our theory and experiments.

We investigate how asymmetrizing an impurity function affects the choice of optimal node splits when growing a decision tree for binary classification. In particular, we relax the usual axioms of an impurity function and show how skewing an impurity function biases the optimal splits to isolate points of a particular class when splitting a node. We give a rigorous definition of this notion, then give a necessary and sufficient condition for such a bias to hold. We also show that the technique of class weighting is equivalent to applying a specific transformation to the impurity function, and tie all these notions together for a class of impurity functions that includes the entropy and Gini impurity. We also briefly discuss cost-insensitive impurity functions and give a characterization of such functions.

Vehicular Ad-hoc NETworks (VANET) can efficiently detect traffic congestion, but detection is not enough because congestion can be further classified as recurrent and non-recurrent congestion (NRC). In particular, NRC in an urban network is mainly caused by incidents, workzones, special events and adverse weather. We propose a framework for the real-time distributed classification of congestion into its components on a heterogeneous urban road network using VANET. We present models built on an understanding of the spatial and temporal causality measures and trained on synthetic data extended from a real case study of Cologne. Our performance evaluation shows a predictive accuracy of 87.63\% for the deterministic Classification Tree (CT), 88.83\% for the Naive Bayesian classifier (NB), 89.51\% for Random Forest (RF) and 89.17\% for the boosting technique. This framework can assist transportation agencies in reducing urban congestion by developing effective congestion mitigation strategies knowing the root causes of congestion.

As one type of machine-learning model, a "decision-tree ensemble model" (DTEM) is represented by a set of decision trees. A DTEM is mainly known to be valid for structured data; however, like other machine-learning models, it is difficult to train so that it returns the correct output value for any input value. Accordingly, when a DTEM is used in regard to a system that requires reliability, it is important to comprehensively detect input values that lead to malfunctions of a system (failures) during development and take appropriate measures. One conceivable solution is to install an input filter that controls the input to the DTEM, and to use separate software to process input values that may lead to failures. To develop the input filter, it is necessary to specify the filtering condition of the input value that leads to the malfunction of the system. Given that necessity, in this paper, we propose a method for formally verifying a DTEM and, according to the result of the verification, if an input value leading to a failure is found, extracting the range in which such an input value exists. The proposed method can comprehensively extract the range in which the input value leading to the failure exists; therefore, by creating an input filter based on that range, it is possible to prevent the failure occurring in the system. In this paper, the algorithm of the proposed method is described, and the results of a case study using a dataset of house prices are presented. On the basis of those results, the feasibility of the proposed method is demonstrated, and its scalability is evaluated.

In this paper, we introduce a framework for solving finite-horizon multistage optimization problems under uncertainty in the presence of auxiliary data. We assume the joint distribution of the uncertain quantities is unknown, but noisy observations, along with observations of auxiliary covariates, are available. We utilize effective predictive methods from machine learning (ML), including $k$-nearest neighbors regression ($k$NN), classification and regression trees (CART), and random forests (RF), to develop specific methods that are applicable to a wide variety of problems. We demonstrate that our solution methods are asymptotically optimal under mild conditions. Additionally, we establish finite sample guarantees for the optimality of our method with $k$NN weight functions. Finally, we demonstrate the practicality of our approach with computational examples. We see a significant decrease in cost by taking into account the auxiliary data in the multistage setting.

Customer behavior is often assumed to follow weak rationality, which implies that adding a product to an assortment will not increase the choice probability of another product in that assortment. However, an increasing amount of research has revealed that customers are not necessarily rational when making decisions. In this paper, we study a new nonparametric choice model that relaxes this assumption and can model a wider range of customer behavior, such as decoy effects between products. In this model, each customer type is associated with a binary decision tree, which represents a decision process for making a purchase based on checking for the existence of specific products in the assortment. Together with a probability distribution over customer types, we show that the resulting model -- a decision forest -- is able to represent any customer choice model, including models that are inconsistent with weak rationality. We theoretically characterize the depth of the forest needed to fit a data set of historical assortments and prove that asymptotically, a forest whose depth scales logarithmically in the number of assortments is sufficient to fit most data sets. We also propose an efficient algorithm for estimating such models from data, based on combining randomization and optimization. Using synthetic data and real transaction data exhibiting non-rational behavior, we show that the model outperforms the multinomial logit and ranking-based models in out-of-sample predictive ability.

In the last few years, there have been many methodological and theoretical advances in the random forests approach. Some methodological developments and extensions include case-specific random forests [19], multivariate random forests [16], quantile regression forests [13], random survival forests [11], enriched random forests for microarry data [1] and predictor augmentation in random forests [18] among others. For theoretical developments, the statistical and asymptotic properties of random forests have been intensively investigated. Advances have been made in the areas such as consistency [2] [15], variable selection [8] and the construction of confidence intervals [17]. Although RF methodology has proven itself to be a reliable predictive approach in many application areas [3][10], there are some cases where random forests may suffer. First, as a fully nonparametric predictive algorithm, random forests may not efficiently incorporate known relationships between the response and the predictors. Second, random forests may fail in extrapolation problems where predictions are required at points out of the domain of the training dataset. For regression problems, a random forest prediction is an average of the predictions produced by the trees in the forest.

Shapelet is a discriminative subsequence of time series. An advanced shapelet-based method is to embed shapelet into accurate and fast random forest. However, it shows several limitations. First, random shapelet forest requires a large training cost for split threshold searching. Second, a single shapelet provides limited information for only one branch of the decision tree, resulting in insufficient accuracy and interpretability. Third, randomized ensemble causes interpretability declining. For that, this paper presents Random Pairwise Shapelets Forest (RPSF). RPSF combines a pair of shapelets from different classes to construct random forest. It omits threshold searching to be more efficient, includes more information for each node of the forest to be more effective. Moreover, a discriminability metric, Decomposed Mean Decrease Impurity (DMDI), is proposed to identify influential region for every class. Extensive experiments show RPSF improves the accuracy and training speed of shapelet-based forest. Case studies demonstrate the interpretability of our method.