Entity Embeddings of Categorical Variables

We map categorical variables in a function approximation problem into Euclidean spaces, which are the entity embeddings of the categorical variables. The mapping is learned by a neural network during the standard supervised training process. Entity embedding not only reduces memory usage and speeds up neural networks compared with one-hot encoding, but more importantly by mapping similar values close to each other in the embedding space it reveals the intrinsic properties of the categorical variables. We applied it successfully in a recent Kaggle competition and were able to reach the third position with relative simple features. We further demonstrate in this paper that entity embedding helps the neural network to generalize better when the data is sparse and statistics is unknown. Thus it is especially useful for datasets with lots of high cardinality features, where other methods tend to overfit. We also demonstrate that the embeddings obtained from the trained neural network boost the performance of all tested machine learning methods considerably when used as the input features instead. As entity embedding defines a distance measure for categorical variables it can be used for visualizing categorical data and for data clustering

Gradient tree boosting with random output projections for multi-label classification and multi-output regression

In many applications of supervised learning, multiple classification or regression outputs have to be predicted jointly. We consider several extensions of gradient boosting to address such problems. We first propose a straightforward adaptation of gradient boosting exploiting multiple output regression trees as base learners. We then argue that this method is only expected to be optimal when the outputs are fully correlated, as it forces the partitioning induced by the tree base learners to be shared by all outputs. We then propose a novel extension of gradient tree boosting to specifically address this issue. At each iteration of this new method, a regression tree structure is grown to fit a single random projection of the current residuals and the predictions of this tree are fitted linearly to the current residuals of all the outputs, independently. Because of this linear fit, the method can adapt automatically to any output correlation structure. Extensive experiments are conducted with this method, as well as other algorithmic variants, on several artificial and real problems. Randomly projecting the output space is shown to provide a better adaptation to different output correlation patterns and is therefore competitive with the best of the other methods in most settings. Thanks to model sharing, the convergence speed is also improved, reducing the computing times (or the complexity of the model) to reach a specific accuracy

Predicting online user behaviour using deep learning algorithms

We propose a robust classifier to predict buying intentions based on user behaviour within a large e-commerce website. In this work we compare traditional machine learning techniques with the most advanced deep learning approaches. We show that both Deep Belief Networks and Stacked Denoising auto-Encoders achieved a substantial improvement by extracting features from high dimensional data during the pre-train phase. They prove also to be more convenient to deal with severe class imbalance.Comment: 21 pages, 3 figures. arXiv admin note: text overlap with arXiv:1412.6601, arXiv:1406.1231, arXiv:1508.03856 by other author

Sparse Projection Oblique Randomer Forests

Decision forests, including Random Forests and Gradient Boosting Trees, have recently demonstrated state-of-the-art performance in a variety of machine learning settings. Decision forests are typically ensembles of axis-aligned decision trees; that is, trees that split only along feature dimensions. In contrast, many recent extensions to decision forests are based on axis-oblique splits. Unfortunately, these extensions forfeit one or more of the favorable properties of decision forests based on axis-aligned splits, such as robustness to many noise dimensions, interpretability, or computational efficiency. We introduce yet another decision forest, called "Sparse Projection Oblique Randomer Forests" (SPORF). SPORF uses very sparse random projections, i.e., linear combinations of a small subset of features. SPORF significantly improves accuracy over existing state-of-the-art algorithms on a standard benchmark suite for classification with >100 problems of varying dimension, sample size, and number of classes. To illustrate how SPORF addresses the limitations of both axis-aligned and existing oblique decision forest methods, we conduct extensive simulated experiments. SPORF typically yields improved performance over existing decision forests, while mitigating computational efficiency and scalability and maintaining interpretability. SPORF can easily be incorporated into other ensemble methods such as boosting to obtain potentially similar gains.Comment: 31 pages; submitted to Journal of Machine Learning Research for revie

ENIGMA-NG: Efficient Neural and Gradient-Boosted Inference Guidance for E

We describe an efficient implementation of clause guidance in saturation-based automated theorem provers extending the ENIGMA approach. Unlike in the first ENIGMA implementation where fast linear classifier is trained and used together with manually engineered features, we have started to experiment with more sophisticated state-of-the-art machine learning methods such as gradient boosted trees and recursive neural networks. In particular the latter approach poses challenges in terms of efficiency of clause evaluation, however, we show that deep integration of the neural evaluation with the ATP data-structures can largely amortize this cost and lead to competitive real-time results. Both methods are evaluated on a large dataset of theorem proving problems and compared with the previous approaches. The resulting methods improve on the manually designed clause guidance, providing the first practically convincing application of gradient-boosted and neural clause guidance in saturation-style automated theorem provers

Learning Feature Nonlinearities with Non-Convex Regularized Binned Regression

For various applications, the relations between the dependent and independent variables are highly nonlinear. Consequently, for large scale complex problems, neural networks and regression trees are commonly preferred over linear models such as Lasso. This work proposes learning the feature nonlinearities by binning feature values and finding the best fit in each quantile using non-convex regularized linear regression. The algorithm first captures the dependence between neighboring quantiles by enforcing smoothness via piecewise-constant/linear approximation and then selects a sparse subset of good features. We prove that the proposed algorithm is statistically and computationally efficient. In particular, it achieves linear rate of convergence while requiring near-minimal number of samples. Evaluations on synthetic and real datasets demonstrate that algorithm is competitive with current state-of-the-art and accurately learns feature nonlinearities. Finally, we explore an interesting connection between the binning stage of our algorithm and sparse Johnson-Lindenstrauss matrices.Comment: 22 pages, 7 figure

Towards Deep and Representation Learning for Talent Search at LinkedIn

Talent search and recommendation systems at LinkedIn strive to match the potential candidates to the hiring needs of a recruiter or a hiring manager expressed in terms of a search query or a job posting. Recent work in this domain has mainly focused on linear models, which do not take complex relationships between features into account, as well as ensemble tree models, which introduce non-linearity but are still insufficient for exploring all the potential feature interactions, and strictly separate feature generation from modeling. In this paper, we present the results of our application of deep and representation learning models on LinkedIn Recruiter. Our key contributions include: (i) Learning semantic representations of sparse entities within the talent search domain, such as recruiter ids, candidate ids, and skill entity ids, for which we utilize neural network models that take advantage of LinkedIn Economic Graph, and (ii) Deep models for learning recruiter engagement and candidate response in talent search applications. We also explore learning to rank approaches applied to deep models, and show the benefits for the talent search use case. Finally, we present offline and online evaluation results for LinkedIn talent search and recommendation systems, and discuss potential challenges along the path to a fully deep model architecture. The challenges and approaches discussed generalize to any multi-faceted search engine.Comment: This paper has been accepted for publication in ACM CIKM 201

Probabilistic Matrix Factorization for Automated Machine Learning

In order to achieve state-of-the-art performance, modern machine learning techniques require careful data pre-processing and hyperparameter tuning. Moreover, given the ever increasing number of machine learning models being developed, model selection is becoming increasingly important. Automating the selection and tuning of machine learning pipelines consisting of data pre-processing methods and machine learning models, has long been one of the goals of the machine learning community. In this paper, we tackle this meta-learning task by combining ideas from collaborative filtering and Bayesian optimization. Using probabilistic matrix factorization techniques and acquisition functions from Bayesian optimization, we exploit experiments performed in hundreds of different datasets to guide the exploration of the space of possible pipelines. In our experiments, we show that our approach quickly identifies high-performing pipelines across a wide range of datasets, significantly outperforming the current state-of-the-art

Learning Nonlinear Functions Using Regularized Greedy Forest

We consider the problem of learning a forest of nonlinear decision rules with general loss functions. The standard methods employ boosted decision trees such as Adaboost for exponential loss and Friedman's gradient boosting for general loss. In contrast to these traditional boosting algorithms that treat a tree learner as a black box, the method we propose directly learns decision forests via fully-corrective regularized greedy search using the underlying forest structure. Our method achieves higher accuracy and smaller models than gradient boosting (and Adaboost with exponential loss) on many datasets

Making Tree Ensembles Interpretable

Tree ensembles, such as random forest and boosted trees, are renowned for their high prediction performance, whereas their interpretability is critically limited. In this paper, we propose a post processing method that improves the model interpretability of tree ensembles. After learning a complex tree ensembles in a standard way, we approximate it by a simpler model that is interpretable for human. To obtain the simpler model, we derive the EM algorithm minimizing the KL divergence from the complex ensemble. A synthetic experiment showed that a complicated tree ensemble was approximated reasonably as interpretable.Comment: presented at 2016 ICML Workshop on Human Interpretability in Machine Learning (WHI 2016), New York, N