Statistical methods for the analysis and forecasting of time series data have a long history (Tsay, 2000). The well-accepted Box-Jenkins analysis and forecasting methods have been applied in a wide range of applications, from finance to medicine, and the classic book that laid out the theory is now in its fourth edition with over 55,000 citations (Box et al., 2015). In this paper, we focus on the specialized area of time series regression where the goal is to predict one time series with the help of covariates that include elements which also have a time series nature. Some authors refer to this as dynamic regression (Hyndman and Athanasopoulos, 2018), others use the term regARIMA (Gómez and Maravall, 1994; Maravall et al., 2016). Pankratz (2012) provides an excellent overview.

Despite the great success of deep learning, recent works show that large deep neural networks are often highly redundant and can be significantly reduced in size. However, the theoretical question of how much we can prune a neural network given a specified tolerance of accuracy drop is still open. This paper provides one answer to this question by proposing a greedy optimization based pruning method. The proposed method has the guarantee that the discrepancy between the pruned network and the original network decays with exponentially fast rate w.r.t. the size of the pruned network, under weak assumptions that apply for most practical settings. Empirically, our method improves prior arts on pruning various network architectures including ResNet, MobilenetV2/V3 on ImageNet.

Dimensionality reduction is a crucial first step for many unsupervised learning tasks including anomaly detection. Autoencoder is a popular mechanism to accomplish the goal of dimensionality reduction. In order to make dimensionality reduction effective for high-dimensional data embedding nonlinear low-dimensional manifold, it is understood that some sort of geodesic distance metric should be used to discriminate the data samples. Inspired by the success of neighborhood aware shortest path based geodesic approximatiors such as ISOMAP, in this work, we propose to use a minimum spanning tree (MST), a graph-based algorithm, to approximate the local neighborhood structure and generate structure-preserving distances among data points. We use this MST-based distance metric to replace the Euclidean distance metric in the embedding function of autoencoders and develop a new graph regularized autoencoder, which outperforms, over 20 benchmark anomaly detection datasets, the plain autoencoder using no regularizer as well as the autoencoders using the Euclidean-based regularizer. We furthermore incorporate the MST regularizer into two generative adversarial networks and find that using the MST regularizer improves the performance of anomaly detection substantially for both generative adversarial networks.

Weakly Labelled learning has garnered lot of attention in recent years due to its potential to scale Sound Event Detection (SED) and is formulated as Multiple Instance Learning (MIL) problem. This paper proposes a Multi-Task Learning (MTL) framework for learning from Weakly Labelled Audio data which encompasses the traditional MIL setup. To show the utility of proposed framework, we use the input TimeFrequency representation (T-F) reconstruction as the auxiliary task. We show that the chosen auxiliary task de-noises internal T-F representation and improves SED performance under noisy recordings. Our second contribution is introducing two step Attention Pooling mechanism. By having 2-steps in attention mechanism, the network retains better T-F level information without compromising SED performance. The visualisation of first step and second step attention weights helps in localising the audio-event in T-F domain. For evaluating the proposed framework, we remix the DCASE 2019 task 1 acoustic scene data with DCASE 2018 Task 2 sounds event data under 0, 10 and 20 db SNR resulting in a multi-class Weakly labelled SED problem. The proposed total framework outperforms existing benchmark models over all SNRs, specifically 22.3 %, 12.8 %, 5.9 % improvement over benchmark model on 0, 10 and 20 dB SNR respectively. We carry out ablation study to determine the contribution of each auxiliary task and 2-step Attention Pooling to the SED performance improvement. The code is publicly released

Modern machine learning workloads use large models, with complex structures, that are very expensive to execute. The devices that execute complex models are becoming increasingly heterogeneous as we see a flourishing of domain-specific accelerators being offered as hardware accelerators in addition to CPUs. These trends necessitate distributing the workload across multiple devices. Recent work has shown that significant gains can be obtained with model parallelism, i.e, partitioning a neural network's computational graph onto multiple devices. In particular, this form of parallelism assumes a pipeline of devices, which is fed a stream of samples and yields high throughput for training and inference of DNNs. However, for such settings (large models and multiple heterogeneous devices), we require automated algorithms and toolchains that can partition the ML workload across devices. In this paper, we identify and isolate the structured optimization problem at the core of device placement of DNN operators, for both inference and training, especially in modern pipelined settings. We then provide algorithms that solve this problem to optimality. We demonstrate the applicability and efficiency of our approaches using several contemporary DNN computation graphs.

Recently, there has been a surge of interest in combining deep learning models with reasoning in order to handle more sophisticated learning tasks. In many cases, a reasoning task can be solved by an iterative algorithm. This algorithm is often unrolled, and used as a specialized layer in the deep architecture, which can be trained end-to-end with other neural components. Although such hybrid deep architectures have led to many empirical successes, the theoretical foundation of such architectures, especially the interplay between algorithm layers and other neural layers, remains largely unexplored. In this paper, we take an initial step towards an understanding of such hybrid deep architectures by showing that properties of the algorithm layers, such as convergence, stability, and sensitivity, are intimately related to the approximation and generalization abilities of the end-to-end model. Furthermore, our analysis matches closely our experimental observations under various conditions, suggesting that our theory can provide useful guidelines for designing deep architectures with reasoning layers.

Invariance and stability are essential notions in dynamical systems study, and thus it is of great interest to learn a dynamics model with a stable invariant set. However, existing methods can only handle the stability of an equilibrium. In this paper, we propose a method to ensure that a dynamics model has a stable invariant set of general classes such as limit cycles and line attractors. We start with the approach by Manek and Kolter (2019), where they use a learnable Lyapunov function to make a model stable with regard to an equilibrium. We generalize it for general sets by introducing projection onto them. To resolve the difficulty of specifying a to-be stable invariant set analytically, we propose defining such a set as a primitive shape (e.g., sphere) in a latent space and learning the transformation between the original and latent spaces. It enables us to compute the projection easily, and at the same time, we can maintain the model's flexibility using various invertible neural networks for the transformation. We present experimental results that show the validity of the proposed method and the usefulness for long-term prediction.

Data corruption is an impediment to modern machine learning deployments. Corrupted data can severely bias the learned model and can also lead to invalid inferences. We present, Picket, a simple framework to safeguard against data corruptions during both training and deployment of machine learning models over tabular data. For the training stage, Picket identifies and removes corrupted data points from the training data to avoid obtaining a biased model. For the deployment stage, Picket flags, in an online manner, corrupted query points to a trained machine learning model that due to noise will result in incorrect predictions. To detect corrupted data, Picket uses a self-supervised deep learning model for mixed-type tabular data, which we call PicketNet. To minimize the burden of deployment, learning a PicketNet model does not require any human-labeled data. Picket is designed as a plugin that can increase the robustness of any machine learning pipeline. We evaluate Picket on a diverse array of real-world data considering different corruption models that include systematic and adversarial noise during both training and testing. We show that Picket consistently safeguards against corrupted data during both training and deployment of various models ranging from SVMs to neural networks, beating a diverse array of competing methods that span from data quality validation models to robust outlier-detection models.

Compressing large neural networks is an important step for their deployment in resource-constrained computational platforms. In this context, vector quantization is an appealing framework that expresses multiple parameters using a single code, and has recently achieved state-of-the-art network compression on a range of core vision and natural language processing tasks. Key to the success of vector quantization is deciding which parameter groups should be compressed together. Previous work has relied on heuristics that group the spatial dimension of individual convolutional filters, but a general solution remains unaddressed. This is desirable for pointwise convolutions (which dominate modern architectures), linear layers (which have no notion of spatial dimension), and convolutions (when more than one filter is compressed to the same codeword). In this paper we make the observation that the weights of two adjacent layers can be permuted while expressing the same function. We then establish a connection to rate-distortion theory and search for permutations that result in networks that are easier to compress. Finally, we rely on an annealed quantization algorithm to better compress the network and achieve higher final accuracy. We show results on image classification, object detection, and segmentation, reducing the gap with the uncompressed model by 40 to 70% with respect to the current state of the art.

We consider compressive sensing in the scenario where the sparsity basis (dictionary) is not known in advance, but needs to be learned from examples. Motivated by the well-known iterative soft thresholding algorithm for the reconstruction, we define deep networks parametrized by the dictionary, which we call deep thresholding networks. Based on training samples, we aim at learning the optimal sparsifying dictionary and thereby the optimal network that reconstructs signals from their low-dimensional linear measurements. The dictionary learning is performed via minimizing the empirical risk. We derive generalization bounds by analyzing the Rademacher complexity of hypothesis classes consisting of such deep networks. We obtain estimates of the sample complexity that depend only linearly on the dimensions and on the depth.