During recent years there has been an increased interest in stochastic adaptations of limited memory quasi-Newton methods, which compared to pure gradient-based routines can improve the convergence by incorporating second order information. In this work we propose a direct least-squares approach conceptually similar to the limited memory quasi-Newton methods, but that computes the search direction in a slightly different way. This is achieved in a fast and numerically robust manner by maintaining a Cholesky factor of low dimension. This is combined with a stochastic line search relying upon fulfilment of the Wolfe condition in a backtracking manner, where the step length is adaptively modified with respect to the optimisation progress. We support our new algorithm by providing several theoretical results guaranteeing its performance. The performance is demonstrated on real-world benchmark problems which shows improved results in comparison with already established methods.

Although stochastic gradient descent (SGD) is a driving force behind the recent success of deep learning, our understanding of its dynamics in a high-dimensional parameter space is limited. In recent years, some researchers have used the stochasticity of minibatch gradients, or the signal-to-noise ratio, to better characterize the learning dynamics of SGD. Inspired from these work, we here analyze SGD from a geometrical perspective by inspecting the stochasticity of the norms and directions of minibatch gradients. We propose a model of the directional concentration for minibatch gradients through von Mises-Fisher (VMF) distribution, and show that the directional uniformity of minibatch gradients increases over the course of SGD. We empirically verify our result using deep convolutional networks and observe a higher correlation between the gradient stochasticity and the proposed directional uniformity than that against the gradient norm stochasticity, suggesting that the directional statistics of minibatch gradients is a major factor behind SGD. Stochastic gradient descent (SGD) has been a driving force behind the recent success of deep learning.

Having the right assortment of shipping boxes in the fulfillment warehouse to pack and ship customer's online orders is an indispensable and integral part of nowadays eCommerce business, as it will not only help maintain a profitable business but also create great experiences for customers. However, it is an extremely challenging operations task to strategically select the best combination of tens of box sizes from thousands of feasible ones to be responsible for hundreds of thousands of orders daily placed on millions of inventory products. In this paper, we present a machine learning approach to tackle the task by formulating the box design problem prescriptively as a generalized version of weighted k-medoids clustering problem, where the parameters are estimated through a variety of descriptive analytics. We test this machine learning approach on fulfillment data collected from Walmart U.S. eCommerce, and our approach is shown to be capable of improving the box utilization rate by more than 10%. Keywords: Shipping box design, k-medoids clustering, eCommerce, packaging science, operations research 1 Introduction The assortment of shipping boxes utilized by the fulfillment warehouse to pack and ship customer's online orders is a critical component of nowadays eCommerce business, as it will directly affect not only profit margins but also customer's experience.

Neural networks are among the most accurate supervised learning methods in use today. However, their opacity makes them difficult to trust in critical applications, especially when conditions in training may differ from those in practice. Recent efforts to develop explanations for neural networks and machine learning models more generally have produced tools to shed light on the implicit rules behind predictions. These tools can help us identify when models are right for the wrong reasons. However, they do not always scale to explaining predictions for entire datasets, are not always at the right level of abstraction, and most importantly cannot correct the problems they reveal. In this thesis, we explore the possibility of training machine learning models (with a particular focus on neural networks) using explanations themselves. We consider approaches where models are penalized not only for making incorrect predictions but also for providing explanations that are either inconsistent with domain knowledge or overly complex. These methods let us train models which can not only provide more interpretable rationales for their predictions but also generalize better when training data is confounded or meaningfully different from test data (even adversarially so).

The use of imitation learning to learn a single policy for a complex task that has multiple modes or hierarchical structure can be challenging. In fact, previous work has shown that when the modes are known, learning separate policies for each mode or sub-task can greatly improve the performance of imitation learning. In this work, we discover the interaction between sub-tasks from their resulting state-action trajectory sequences using a directed graphical model. We propose a new algorithm based on the generative adversarial imitation learning framework which automatically learns sub-task policies from unsegmented demonstrations. Our approach maximizes the directed information flow in the graphical model between sub-task latent variables and their generated trajectories. We also show how our approach connects with the existing Options framework, which is commonly used to learn hierarchical policies.

Image source: Glenfinnan Viaduct – aka "The Harry Potter Bridge" source Wikipedia – an apt analogy bridging the known to the unknown! In April this year, I posted about the seven books to grasp the mathematical foundations of data science which was one of my most popular posts ever. It demonstrated to me that there is a real need to understand the maths foundations behind Data Science. As part of my teaching at the University of Oxford(Data Science for Internet of Things), I have often encountered the same issue in working with participants. I am also personally interested in democratising AI knowledge, especially for the younger generation.

Spark library has a library for ML labelled as MLib. This Apache Spark library has algorithms for the functions of classification, regression, clustering, collaborative filtering, dimensionality reduction, etc. The classification includes classifying things into different categories. For example, in emails the classification is done in categories of inbox, sent, drafts, spam and so on. Clustering example is bifurcating the news on the basis of the title and content of the news.

Gradient-based meta-learning techniques are both widely applicable and proficient at solving challenging few-shot learning and fast adaptation problems. However, they have practical difficulties when operating on high-dimensional parameter spaces in extreme low-data regimes. We show that it is possible to bypass these limitations by learning a data-dependent latent generative representation of model parameters, and performing gradient-based meta-learning in this lowdimensional latent space. Our evaluation shows that LEO can achieve state-of-the-art performance on the competitive miniImageNet and tieredImageNet few-shot classification tasks. Further analysis indicates LEO is able to capture uncertainty in the data, and can perform adaptation more effectively by optimizing in latent space. Humans have a remarkable ability to quickly grasp new concepts from a very small number of examples or a limited amount of experience, leveraging prior knowledge and context. Just as humans can efficiently learn new tasks, it is desirable for learning algorithms to quickly adapt to and incorporate new and unseen information. Few-shot learning tasks challenge models to learn a new concept or behaviour with very few examples or limited experience (Fei-Fei et al., 2006; Lake et al., 2011).

With the rapid development of high-throughput technologies, parallel acquisition of large-scale drug-informatics data provides huge opportunities to improve pharmaceutical research and development. One significant application is the purpose prediction of small molecule compounds, aiming to specify therapeutic properties of extensive purpose-unknown compounds and to repurpose novel therapeutic properties of FDA-approved drugs. Such problem is very challenging since compound attributes contain heterogeneous data with various feature patterns such as drug fingerprint, drug physicochemical property, drug perturbation gene expression. Moreover, there is complex nonlinear dependency among heterogeneous data. In this paper, we propose a novel domain-adversarial multi-task framework for integrating shared knowledge from multiple domains. The framework utilizes the adversarial strategy to effectively learn target representations and models their nonlinear dependency. Experiments on two real-world datasets illustrate that the performance of our approach obtains an obvious improvement over competitive baselines. The novel therapeutic properties of purpose-unknown compounds we predicted are mostly reported or brought to the clinics. Furthermore, our framework can integrate various attributes beyond the three domains examined here and can be applied in the industry for screening the purpose of huge amounts of as yet unidentified compounds. Source codes of this paper are available on Github.

In many applications we seek to maximize an expectation with respect to a distribution over discrete variables. Estimating gradients of such objectives with respect to the distribution parameters is a challenging problem. We analyze existing solutions including finite-difference (FD) estimators and continuous relaxation (CR) estimators in terms of bias and variance. We show that the commonly used Gumbel-Softmax estimator is biased and propose a simple method to reduce it. We also derive a simpler piece-wise linear continuous relaxation that also possesses reduced bias. We demonstrate empirically that reduced bias leads to a better performance in variational inference and on binary optimization tasks. Discrete stochastic variables arise naturally for certain types of data, and distributions over discrete variables can be important components of probabilistic models. Eq. (1) is commonly minimized by gradient-based methods, which require estimating the gradient The two main approaches to this problem are score function estimators and pathwise derivative estimators(see Schulman et al. (2015) for an overview). In this paper we focus on pathwise derivative estimators. This approach is applicable to cases in which the stochastic variables can be reparameterized as a function of other parameter-independent random variables, i.e. z g However, for discrete variables the cumulative distribution function (CDF) is discontinuous and reparameterization is not possible.