We show the equivalence of discrete choice models and the class of binary choice forests, which are random forest based on binary choice trees. This suggests that standard machine learning techniques based on random forest can serve to estimate discrete choice model with an interpretable output. This is confirmed by our data driven result that states that random forest can accurately predict the choice probability of any discrete choice model. Our framework has unique advantages: it can capture behavioral patterns such as irrationality or sequential searches; it handles nonstandard formats of training data that result from aggregation; it can measure product importance based on how frequently a random customer would make decisions depending on the presence of the product; it can also incorporate price information. Our numerical results show that binary choice forest can outperform the best parametric models with much better computational times.

We study the relationship between catastrophic forgetting and properties of task sequences. In particular, given a sequence of tasks, we would like to understand which properties of this sequence influence the error rates of continual learning algorithms trained on the sequence. To this end, we propose a new procedure that makes use of recent developments in task space modeling as well as correlation analysis to specify and analyze the properties we are interested in. As an application, we apply our procedure to study two properties of a task sequence: (1) total complexity and (2) sequential heterogeneity. We show that error rates are strongly and positively correlated to a task sequence's total complexity for some state-of-the-art algorithms. We also show that, surprisingly, the error rates have no or even negative correlations in some cases to sequential heterogeneity. Our findings suggest directions for improving continual learning benchmarks and methods.

Networks are a natural representation of complex systems across the sciences, and higher-order dependencies are central to the understanding and modeling of these systems. However, in many practical applications such as online social networks, networks are massive, dynamic, and naturally streaming, where pairwise interactions become available one at a time in some arbitrary order. The massive size and streaming nature of these networks allow only partial observation, since it is infeasible to analyze the entire network. Under such scenarios, it is challenging to study the higher-order structural and connectivity patterns of streaming networks. In this work, we consider the fundamental problem of estimating the higher-order dependencies using adaptive sampling. We propose a novel adaptive, single-pass sampling framework and unbiased estimators for higher-order network analysis of large streaming networks. Our algorithms exploit adaptive techniques to identify edges that are highly informative for efficiently estimating the higher-order structure of streaming networks from small sample data. We also introduce a novel James-Stein-type shrinkage estimator to minimize the estimation error. Our approach is fully analytic with theoretical guarantees, computationally efficient, and can be incrementally updated in a streaming setting. Numerical experiments on large networks show that our approach is superior to baseline methods.

Traditionally, music was treated as an analogue signal and was generated manually. In recent years, music is conspicuous to technology which can generate a suite of music automatically without any human intervention. To accomplish this task, we need to overcome some technical challenges which are discussed descriptively in this paper. A brief introduction about music and its components is provided in the paper along with the citation and analysis of related work accomplished by different authors in this domain. Main objective of this paper is to propose an algorithm which can be used to generate musical notes using Recurrent Neural Networks (RNN), principally Long Short-Term Memory (LSTM) networks. A model is designed to execute this algorithm where data is represented with the help of musical instrument digital interface (MIDI) file format for easier access and better understanding. Preprocessing of data before feeding it into the model, revealing methods to read, process and prepare MIDI files for input are also discussed. The model used in this paper is used to learn the sequences of polyphonic musical notes over a single-layered LSTM network. The model must have the potential to recall past details of a musical sequence and its structure for better learning. Description of layered architecture used in LSTM model and its intertwining connections to develop a neural network is presented in this work. This paper imparts a peek view of distributions of weights and biases in every layer of the model along with a precise representation of losses and accuracy at each step and batches. When the model was thoroughly analyzed, it produced stellar results in composing new melodies.

Model quantization is leveraged to reduce the memory consumption and the computation time of deep neural networks. This is achieved by representing weights and activations with a lower bit resolution when compared to their high precision floating point counterparts. The suitable level of quantization is directly related to the model performance. Lowering the quantization precision (e.g. 2 bits), reduces the amount of memory required to store model parameters and the amount of logic required to implement computational blocks, which contributes to reducing the power consumption of the entire system. These benefits typically come at the cost of reduced accuracy. The main challenge is to quantize a network as much as possible, while maintaining the performance accuracy. In this work, we present a quantization method for the U-Net architecture, a popular model in medical image segmentation. We then apply our quantization algorithm to three datasets: (1) the Spinal Cord Gray Matter Segmentation (GM), (2) the ISBI challenge for segmentation of neuronal structures in Electron Microscopic (EM), and (3) the public National Institute of Health (NIH) dataset for pancreas segmentation in abdominal CT scans. The reported results demonstrate that with only 4 bits for weights and 6 bits for activations, we obtain 8 fold reduction in memory requirements while loosing only 2.21%, 0.57% and 2.09% dice overlap score for EM, GM and NIH datasets respectively. Our fixed point quantization provides a flexible trade off between accuracy and memory requirement which is not provided by previous quantization methods for U-Net such as TernaryNet.

Falls prevention, especially in older people, becomes an increasingly important topic in the times of aging societies. In this work, we present Gated Recurrent Unit-based neural networks models designed for predicting falls (syncope). The cardiovascular systems signals used in the study come from Gravitational Physiology, Aging and Medicine Research Unit, Institute of Physiology, Medical University of Graz. We used two of the collected signals, heart rate, and mean blood pressure. By using bidirectional GRU model, it was possible to predict the syncope occurrence approximately ten minutes before the manual marker.

Clustering time series is a delicate task; varying lengths and temporal offsets obscure direct comparisons. A natural strategy is to learn a parametric model foreach time series and to cluster the model parameters rather than the sequences themselves. Linear dynamical systems are a fundamental and powerful parametric model class. However, identifying the parameters of a linear dynamical systems is a venerable task, permitting provably efficient solutions only in special cases. In this work, we show that clustering the parameters of unknown linear dynamical systems is, in fact, easier than identifying them. We analyze a computationally efficient clustering algorithm that enjoys provable convergence guarantees under a natural separation assumption. Although easy to implement, our algorithm is general, handling multi-dimensional data with time offsets and partial sequences. Evaluating our algorithm on both synthetic data and real electrocardiogram (ECG) signals, we see significant improvements in clustering quality over existing baselines.

We study the problem of estimating the parameters of a Gaussian distribution when samples are only shown if they fall in some (unknown) subset $S \subseteq \R^d$. This core problem in truncated statistics has long history going back to Galton, Lee, Pearson and Fisher. Recent work by Daskalakis et al. (FOCS'18), provides the first efficient algorithm that works for arbitrary sets in high dimension when the set is known, but leaves as an open problem the more challenging and relevant case of unknown truncation set. Our main result is a computationally and sample efficient algorithm for estimating the parameters of the Gaussian under arbitrary unknown truncation sets whose performance decays with a natural measure of complexity of the set, namely its Gaussian surface area. Notably, this algorithm works for large families of sets including intersections of halfspaces, polynomial threshold functions and general convex sets. We show that our algorithm closely captures the tradeoff between the complexity of the set and the number of samples needed to learn the parameters by exhibiting a set with small Gaussian surface area for which it is information theoretically impossible to learn the true Gaussian with few samples.

In this paper we study the matrix completion problem: Suppose $X \in \mathbb{R}^{n_r \times n_c}$ is unknown except for an upper bound $r$ on its rank. By measuring a small number $m \ll n_r n_c$ of elements of $X$, is it possible to recover $X$ exactly, or at least, to construct a reasonable approximation of $X$? There are two approaches to choosing the sample set, namely probabilistic and deterministic. At present there are very few deterministic methods, and they apply only to square matrices. The focus in the present paper is on deterministic methods that work for rectangular as well as square matrices. The elements to be sampled are chosen as the edge set of an asymmetric Ramanujan graph. For such a measurement matrix, we derive bounds on the error between a scaled version of the sampled matrix and unknown matrix, and show that, under suitable conditions, the unknown matrix can be recovered exactly. Even for the case of square matrices, these bounds are an improvement on known results. Of course they are entirely new for rectangular matrices. This raises the question of how such asymmetric Ramanujan graphs might be constructed. While some techniques exist for constructing Ramanujan bipartite graphs with equal numbers of vertices on both sides, until now no methods exist for constructing Ramanujan bipartite graphs with unequal numbers of vertices on the two sides. We provide a method for the construction of an infinite family of asymmetric biregular Ramanujan graphs with $q^2$ left vertices and $lq$ right vertices, where $q$ is any prime number and $l$ is any integer between $2$ and $q$. The left degree is $l$ and the right degree is $q$. So far as the authors are aware, this is the first explicit construction of an infinite family of asymmetric Ramanujan graphs.

Understanding the connectivity in the brain is an important prerequisite for understanding how the brain processes information. In the Brain/MINDS project, a connectivity study on marmoset brains uses two-photon microscopy fluorescence images of axonal projections to collect the neuron connectivity from defined brain regions at the mesoscopic scale. The processing of the images requires the detection and segmentation of the axonal tracer signal. The objective is to detect as much tracer signal as possible while not misclassifying other background structures as the signal. This can be challenging because of imaging noise, a cluttered image background, distortions or varying image contrast cause problems. We are developing MarmoNet, a pipeline that processes and analyzes tracer image data of the common marmoset brain. The pipeline incorporates state-of-the-art machine learning techniques based on artificial convolutional neural networks (CNN) and image registration techniques to extract and map all relevant information in a robust manner. The pipeline processes new images in a fully automated way. This report introduces the current state of the tracer signal analysis part of the pipeline.