A high-level machine learning library that allows you to build programs that learn from data using the PHP language. Machine learning is the process by which a computer program is able to progressively improve performance on a certain task through training and data without explicitly being programmed. There are two types of machine learning that Rubix supports out of the box, Supervised and Unsupervised. Machine learning projects typically begin with a question. For example, you might want to answer the question "who of my friends are most likely to stay married to their spouse?" One way to go about answering this question with machine learning would be to go out and ask a bunch of happily married and divorced couples the same set of questions about their partner and then use that data to build a model of what a successful marriage looks like. Later, you can use that model to make predictions based on the answers you get from your friends. Specifically, the answers you collect are ...

Clustering is a powerful unsupervised knowledge discovery tool used today, which aims to segment your data points into groups of similar features. However, each algorithm is pretty sensitive to the parameters. Similarity based techniques (K-means, etc) are tasked with designating how many clusters exist, while hierarchical usually require manual intervention to decide when to assign finished clusters. The most common density based approach, DBSCAN, requires only two parameters pertaining to how it defines its "Core Points", but finding the parameters can often be an extremely difficult task. It also will not be able to find clusters of differing densities. There is a relative of DBSCAN, called OPTICS (Ordering Points to Identify Cluster Structure), that invokes a different process.

This is the third post in the optimization series, where we are trying to give the reader a comprehensive review of optimization in deep learning. Mini Batch Gradient Descent is used to combat local minima, and saddle points. How adaptive methods like Momentum, RMSProp and Adam, augment vanilla Gradient Descent to address the problem of pathological curvature. Neural networks, unlike the machine learning methods that came before it do not rest upon any probabilistic or statistical assumptions about the data they are fed. However, one of the most, if not the most important element required to ensure that neural networks learn properly is that the data fed to the layers of a neural network exhibit certain properties. In this article, we will cover problems No. 1 and 2, and how activation functions are used to address them.

A recommender system is an information filtering technology which can be used to predict preference ratings of items (products, services, movies, etc) and/or to output a ranking of items that are likely to be of interest to the user. Context-aware recommender systems (CARS) learn and predict the tastes and preferences of users by incorporating available contextual information in the recommendation process. One of the major challenges in context-aware recommender systems research is the lack of automatic methods to obtain contextual information for these systems. Considering this scenario, in this paper, we propose to use contextual information from topic hierarchies of the items (web pages) to improve the performance of context-aware recommender systems. The topic hierarchies are constructed by an extension of the LUPI-based Incremental Hierarchical Clustering method that considers three types of information: traditional bag-of-words (technical information), and the combination of named entities (privileged information I) with domain terms (privileged information II). We evaluated the contextual information in four context-aware recommender systems. Different weights were assigned to each type of information. The empirical results demonstrated that topic hierarchies with the combination of the two kinds of privileged information can provide better recommendations.

Material scientists are increasingly adopting the use of machine learning (ML) for making potentially important decisions, such as, discovery, development, optimization, synthesis and characterization of materials. However, despite ML's impressive performance in commercial applications, several unique challenges exist when applying ML in materials science applications. In such a context, the contributions of this work are twofold. First, we identify common pitfalls of existing ML techniques when learning from underrepresented/imbalanced material data. Specifically, we show that with imbalanced data, standard methods for assessing quality of ML models break down and lead to misleading conclusions. Furthermore, we found that the model's own confidence score cannot be trusted and model introspection methods (using simpler models) do not help as they result in loss of predictive performance (reliability-explainability trade-off). Second, to overcome these challenges, we propose a general-purpose explainable and reliable machine-learning framework. Specifically, we propose a novel pipeline that employs an ensemble of simpler models to reliably predict material properties. We also propose a transfer learning technique and show that the performance loss due to models' simplicity can be overcome by exploiting correlations among different material properties. A new evaluation metric and a trust score to better quantify the confidence in the predictions are also proposed. To improve the interpretability, we add a rationale generator component to our framework which provides both model-level and decision-level explanations. Finally, we demonstrate the versatility of our technique on two applications: 1) predicting properties of crystalline compounds, and 2) identifying novel potentially stable solar cell materials.

With the development of multimedia era, multi-view data is generated in various fields. Contrast with those single-view data, multi-view data brings more useful information and should be carefully excavated. Therefore, it is essential to fully exploit the complementary information embedded in multiple views to enhance the performances of many tasks. Especially for those high-dimensional data, how to develop a multi-view dimension reduction algorithm to obtain the low-dimensional representations is of vital importance but chanllenging. In this paper, we propose a novel multi-view dimensional reduction algorithm named Auto-weighted Mutli-view Sparse Reconstructive Embedding (AMSRE) to deal with this problem. AMSRE fully exploits the sparse reconstructive correlations between features from multiple views. Furthermore, it is equipped with an auto-weighted technique to treat multiple views discriminatively according to their contributions. Various experiments have verified the excellent performances of the proposed AMSRE.

In this paper, we propose a method for clustering image-caption pairs by simultaneously learning image representations and text representations that are constrained to exhibit similar distributions. These image-caption pairs arise frequently in high-value applications where structured training data is expensive to produce but free-text descriptions are common. MultiDEC initializes parameters with stacked autoencoders, then iteratively minimizes the Kullback-Leibler divergence between the distribution of the images (and text) to that of a combined joint target distribution. We regularize by penalizing non-uniform distributions across clusters. The representations that minimize this objective produce clusters that outperform both single-view and multi-view techniques on large benchmark image-caption datasets.

We consider the problem of multi-product dynamic pricing in a contextual setting for a seller of differentiated products. In this environment, the customers arrive over time and products are described by high-dimensional feature vectors. Each customer chooses a product according to the widely used Multinomial Logit (MNL) choice model and her utility depends on the product features as well as the prices offered. Our model allows for heterogenous price sensitivities for products. The seller a-priori does not know the parameters of the choice model but can learn them through interactions with the customers. The seller's goal is to design a pricing policy that maximizes her cumulative revenue. This model is motivated by online marketplaces such as Airbnb platform and online advertising. We measure the performance of a pricing policy in terms of regret, which is the expected revenue loss with respect to a clairvoyant policy that knows the parameters of the choice model in advance and always sets the revenue-maximizing prices. We propose a pricing policy, named M3P, that achieves a $T$-period regret of $O(\sqrt{\log(dT) T})$ under heterogenous price sensitivity for products with features dimension of $d$. We also prove that no policy can achieve worst-case $T$-regret better than $\Omega(\sqrt{T})$.

Recently, there has been emerging interest in constructing reproducing kernel Banach spaces (RKBS) for applied and theoretical purposes such as machine learning, sampling reconstruction, sparse approximation and functional analysis. Existing constructions include the reflexive RKBS via a bilinear form, the semi-inner-product RKBS, the RKBS with $\ell^1$ norm, the $p$-norm RKBS via generalized Mercer kernels, etc. The definitions of RKBS and the associated reproducing kernel in those references are dependent on the construction. Moreover, relations among those constructions are unclear. We explore a generic definition of RKBS and the reproducing kernel for RKBS that is independent of construction. Furthermore, we propose a framework of constructing RKBSs that unifies existing constructions mentioned above via a continuous bilinear form and a pair of feature maps. A new class of Orlicz RKBSs is proposed. Finally, we develop representer theorems for machine learning in RKBSs constructed in our framework, which also unifies representer theorems in existing RKBSs.

The model interpretation is essential in many application scenarios and to build a classification model with a ease of model interpretation may provide useful information for further studies and improvement. It is common to encounter with a lengthy set of variables in modern data analysis, especially when data are collected in some automatic ways. This kinds of datasets may not collected with a specific analysis target and usually contains redundant features, which have no contribution to a the current analysis task of interest. Variable selection is a common way to increase the ability of model interpretation and is popularly used with some parametric classification models. There is a lack of studies about variable selection in nonparametric classification models such as the density estimation-based methods and this is especially the case for multiple-class classification situations. In this study we study multiple-class classification problems using the thought of sparse non-parametric density estimation and propose a method for identifying high impacts variables for each class. We present the asymptotic properties and the computation procedure for the proposed method together with some suggested sample size. We also repost the numerical results using both synthesized and some real data sets.