Applied Data Scientists throughout various industries are commonly faced with the challenging task of encoding high-cardinality categorical features into digestible inputs for machine learning algorithms. This paper describes a Bayesian encoding technique developed for WeWork's lead scoring engine which outputs the probability of a person touring one of our office spaces based on interaction, enrichment, and geospatial data. We present a paradigm for ensemble modeling which mitigates the need to build complicated preprocessing and encoding schemes for categorical variables. In particular, domain-specific conjugate Bayesian models are employed as base learners for features in a stacked ensemble model. For each column of a categorical feature matrix we fit a problem-specific prior distribution, for example, the Beta distribution for a binary classification problem. In order to analytically derive the moments of the posterior distribution, we update the prior with the conjugate likelihood of the corresponding target variable for each unique value of the given categorical feature. This function of column and value encodes the categorical feature matrix so that the final learner in the ensemble model ingests low-dimensional numerical input. Experimental results on both curated and real world datasets demonstrate impressive accuracy and computational efficiency on a variety of problem archetypes. Particularly, for the lead scoring engine at WeWork -- where some categorical features have as many as 300,000 levels -- we have seen an AUC improvement from 0.87 to 0.97 through implementing conjugate Bayesian model encoding.
Weinberger, K. et al propose a method for dimensionality reduction which they call the hashing trick @cite_10 . In this approach hashing techniques are used to map the feature space to a reduced vector space. This has the desirable effect of not only reducing dimensionality and therefore computation, but it also provides an elegant way of dealing with new or missing entries. One shortcoming is the presence of collision where different entries are assigned the same hash. However it has been shown the the gain in accuracy and performance outweigh the effects of this phenomenon.
@cite_10
2953133476 2051666324 1959016151 2261895596
Empirical evidence suggests that hashing is an effective strategy for dimensionality reduction and practical nonparametric estimation. In this paper we provide exponential tail bounds for feature hashing and show that the interaction between random subspaces is negligible with high probability. We demonstrate the feasibility of this approach with experimental results for a new use case -- multitask learning with hundreds of thousands of tasks. Previous efforts in hashing intend to preserve data variance or pairwise affinity, but neither is adequate in capturing the manifold structures hidden in most visual data. In this paper, we tackle this problem by reconstructing the locally linear structures of manifolds in the binary Hamming space, which can be learned by locality-sensitive sparse coding. We cast the problem as a joint minimization of reconstruction error and quantization loss, and show that, despite its NP-hardness, a local optimum can be obtained efficiently via alternative optimization. Our method distinguishes itself from existing methods in its remarkable ability to extract the nearest neighbors of the query from the same manifold, instead of from the ambient space. On extensive experiments on various image benchmarks, our results improve previous state-of-the-art by 28-74 typically, and 627 on the Yale face data. Retrieving videos of a specific person given his her face image as query becomes more and more appealing for applications like smart movie fast-forwards and suspect searching. It also forms an interesting but challenging computer vision task, as the visual data to match, i.e., still image and video clip are usually represented quite differently. Typically, face image is represented as point (i.e., vector) in Euclidean space, while video clip is seemingly modeled as a point (e.g., covariance matrix) on some particular Riemannian manifold in the light of its recent promising success. It thus incurs a new hashing-based retrieval problem of matching two heterogeneous representations, respectively in Euclidean space and Riemannian manifold. This work makes the first attempt to embed the two heterogeneous spaces into a common discriminant Hamming space. Specifically, we propose Hashing across Euclidean space and Riemannian manifold (HER) by deriving a unified framework to firstly embed the two spaces into corresponding reproducing kernel Hilbert spaces, and then iteratively optimize the intra- and inter-space Hamming distances in a max-margin framework to learn the hash functions for the two spaces. Extensive experiments demonstrate the impressive superiority of our method over the state-of-the-art competitive hash learning methods. We consider a new construction of locality-sensitive hash functions for Hamming space that is covering in the sense that is it guaranteed to produce a collision for every pair of vectors within a given radius r. The construction is efficient in the sense that the expected number of hash collisions between vectors at distance cr, for a given c > 1, comes close to that of the best possible data independent LSH without the covering guarantee, namely, the seminal LSH construction of Indyk and Motwani (FOCS '98). The efficiency of the new construction essentially matches their bound if cr = log(n) k, where n is the number of points in the data set and k ∈ N, and differs from it by at most a factor ln(4) in the exponent for general values of cr. As a consequence, LSH-based similarity search in Hamming space can avoid the problem of false negatives at little or no cost in efficiency.