The field of medicine has, arguably, been more positively affected by modern deep learning techniques than any other industry.

This course is focused on the question: How do we do matrix computations with acceptable speed and acceptable accuracy? This course was taught in the University of San Francisco's Masters of Science in Analytics program, summer 2017 (for graduate students studying to become data scientists). The course is taught in Python with Jupyter Notebooks, using libraries such as Scikit-Learn and Numpy for most lessons, as well as Numba (a library that compiles Python to C for faster performance) and PyTorch (an alternative to Numpy for the GPU) in a few lessons. Accompanying the notebooks is a playlist of lecture videos, available on YouTube. If you are ever confused by a lecture or it goes too quickly, check out the beginning of the next video, where I review concepts from the previous lecture, often explaining things from a new perspective or with different illustrations, and answer questions.

Google subsidiary DeepMind today unveiled a new type of computer vision algorithm that can generate 3D models of a scene from 2D snapshots: the Generative Query Network (GQN). The GQN, details of which were published in Science, can "imagine" and render scenes from any angle without any human supervision or training. Given just a handful of pictures of a scene -- a wallpapered room with a colored sphere on the floor, for example -- the algorithm can render opposite, unseen sides of objects and generate a 3D view from multiple vantage points, even accounting for things like lighting in shadows. It aims to replicate the way the human brain learns about its surroundings and the physical interactions between objects, and eliminate the need for AI researchers to annotate images in datasets. Most visual recognition systems require a human to label every aspect of every object in each scene in a dataset, a laborious and costly process.

Quantized Neural Networks (QNNs) are often used to improve network efficiency during the inference phase, i.e. after the network has been trained. Extensive research in the field suggests many different quantization schemes. Still, the number of bits required, as well as the best quantization scheme, are yet unknown. Our theoretical analysis suggests that most of the training process is robust to substantial precision reduction, and points to only a few specific operations that require higher precision. Armed with this knowledge, we quantize the model parameters, activations and layer gradients to 8-bit, leaving at a higher precision only the final step in the computation of the weight gradients. Additionally, as QNNs require batch-normalization to be trained at high precision, we introduce Range Batch-Normalization (BN) which has significantly higher tolerance to quantization noise and improved computational complexity. Our simulations show that Range BN is equivalent to the traditional batch norm if a precise scale adjustment, which can be approximated analytically, is applied. To the best of the authors' knowledge, this work is the first to quantize the weights, activations, as well as a substantial volume of the gradients stream, in all layers (including batch normalization) to 8-bit while showing state-of-the-art results over the ImageNet-1K dataset.

In this paper, we propose multi-variable LSTM capable of accurate forecasting and variable importance interpretation for time series with exogenous variables. Current attention mechanism in recurrent neural networks mostly focuses on the temporal aspect of data and falls short of characterizing variable importance. To this end, the multi-variable LSTM equipped with tensorized hidden states is developed to learn hidden states for individual variables, which give rise to our mixture temporal and variable attention. Based on such attention mechanism, we infer and quantify variable importance. Extensive experiments using real datasets with Granger-causality test and the synthetic dataset with ground truth demonstrate the prediction performance and interpretability of multi-variable LSTM in comparison to a variety of baselines. It exhibits the prospect of multi-variable LSTM as an end-to-end framework for both forecasting and knowledge discovery.

We propose a novel method for compressed sensing recovery using untrained deep generative models. Our method is based on the recently proposed Deep Image Prior (DIP), wherein the convolutional weights of the network are optimized to match the observed measurements. We show that this approach can be applied to solve any differentiable inverse problem. We also introduce a novel learned regularization technique which incorporates a small amount of prior information, further reducing the number of measurements required for a given reconstruction error. Our algorithm requires approximately 4 - 6 fewer measurements than classical Lasso methods. Unlike previous approaches based on generative models, our method does not require the model to be pre-trained. As such, we can apply our method to various medical imaging datasets for which data acquisition is expensive and no known generative models exist.

We develop a fast, tractable technique called Net-Trim for simplifying a trained neural network. The method is a convex post-processing module, which prunes (sparsifies) a trained network layer by layer, while preserving the internal responses. We present a comprehensive analysis of Net-Trim from both the algorithmic and sample complexity standpoints, centered on a fast, scalable convex optimization program. Our analysis includes consistency results between the initial and retrained models before and after Net-Trim application and guarantees on the number of training samples needed to discover a network that can be expressed using a certain number of nonzero terms. Specifically, if there is a set of weights that uses at most $s$ terms that can re-create the layer outputs from the layer inputs, we can find these weights from $\mathcal{O}(s\log N/s)$ samples, where $N$ is the input size. These theoretical results are similar to those for sparse regression using the Lasso, and our analysis uses some of the same recently-developed tools (namely recent results on the concentration of measure and convex analysis). Finally, we propose an algorithmic framework based on the alternating direction method of multipliers (ADMM), which allows a fast and simple implementation of Net-Trim for network pruning and compression.

The holy grail of deep learning is to come up with an automatic method to design optimal architectures for different applications. In other words, how can we effectively dimension and organize neurons along the network layers based on the computational resources, input size, and amount of training data? We outline promising research directions based on polyhedral theory and mixed-integer representability that may offer an analytical approach to this question, in contrast to the empirical techniques often employed.

Feature engineering is one of the most important but most tedious tasks in data science. This work studies automation of feature learning from relational database. We first prove theoretically that finding the optimal features from relational data for predictive tasks is NP-hard. We propose an efficient rule-based approach based on heuristics and a deep neural network to automatically learn appropriate features from relational data. We benchmark our approaches in ensembles in past Kaggle competitions. Our new approach wins late medals and beats the state-of-the-art solutions with significant margins. To the best of our knowledge, this is the first time an automated data science system could win medals in Kaggle competitions with complex relational database.