Our work presents two fundamental contributions. On the application side, we tackle the challenging problem of predicting day-ahead crypto-currency prices. On the methodological side, a new dynamical modeling approach is proposed. Our approach keeps the probabilistic formulation of the state-space model, which provides uncertainty quantification on the estimates, and the function approximation ability of deep neural networks. We call the proposed approach the deep state-space model. The experiments are carried out on established cryptocurrencies (obtained from Yahoo Finance). The goal of the work has been to predict the price for the next day. Benchmarking has been done with both state-of-the-art and classical dynamical modeling techniques. Results show that the proposed approach yields the best overall results in terms of accuracy. Preprint submitted to XXX November 28, 2023 1. Introduction Investopedia defines crypto-currency as "a digital or virtual currency that is secured by cryptography, which makes it nearly impossible to counterfeit or double-spend" and is built on "decentralized networks based on block-chain technology--a distributed ledger enforced by a disparate network of computers". A defining feature of crypto-currencies is that they are usually not issued by central banking agencies like the Federal Reserve System in US, Bank of Canada, European Central Bank, or the People's Bank of China; this makes cryptocurrencies (theoretically) immune to government interventions. The introduction of Bitcoin around 2009 and its meteoric rise led to investors infuse their funds in crypto-currencies.

In this work we propose a clustering framework based on the paradigm of transform learning. In simple terms the representation from transform learning is used for K-means clustering; however, the problem is not solved in such a na\"ive piecemeal fashion. The K-means clustering loss is embedded into the transform learning framework and the joint problem is solved using the alternating direction method of multipliers. Results on document clustering show that our proposed approach improves over the state-of-the-art.

This work introduces a new unsupervised representation learning technique called Deep Convolutional Transform Learning (DCTL). By stacking convolutional transforms, our approach is able to learn a set of independent kernels at different layers. The features extracted in an unsupervised manner can then be used to perform machine learning tasks, such as classification and clustering. The learning technique relies on a well-sounded alternating proximal minimization scheme with established convergence guarantees. Our experimental results show that the proposed DCTL technique outperforms its shallow version CTL, on several benchmark datasets.

Increasing population indicates that energy demands need to be managed in the residential sector. Prior studies have reflected that the customers tend to reduce a significant amount of energy consumption if they are provided with appliance-level feedback. This observation has increased the relevance of load monitoring in today's tech-savvy world. Most of the previously proposed solutions claim to perform load monitoring without intrusion, but they are not completely non-intrusive. These methods require historical appliance-level data for training the model for each of the devices. This data is gathered by putting a sensor on each of the appliances present in the home which causes intrusion in the building. Some recent studies have proposed that if we frame Non-Intrusive Load Monitoring (NILM) as a multi-label classification problem, the need for appliance-level data can be avoided. In this paper, we propose Multi-label Restricted Boltzmann Machine(ML-RBM) for NILM and report an experimental evaluation of proposed and state-of-the-art techniques.

Currently there are two predominant ways to train deep neural networks. The first one uses restricted Boltzmann machine (RBM) and the second one autoencoders. RBMs are stacked in layers to form deep belief network (DBN); the final representation layer is attached to the target to complete the deep neural network. Autoencoders are nested one inside the other to form stacked autoencoders; once the stcaked autoencoder is learnt the decoder portion is detached and the target attached to the deepest layer of the encoder to form the deep neural network. This work proposes a new approach to train deep neural networks using dictionary learning as the basic building block; the idea is to use the features from the shallower layer as inputs for training the next deeper layer. One can use any type of dictionary learning (unsupervised, supervised, discriminative etc.) as basic units till the pre-final layer. In the final layer one needs to use the label consistent dictionary learning formulation for classification. We compare our proposed framework with existing state-of-the-art deep learning techniques on benchmark problems; we are always within the top 10 results. In actual problems of age and gender classification, we are better than the best known techniques.

In this work we propose a new deep learning tool called deep dictionary learning. Multi-level dictionaries are learnt in a greedy fashion, one layer at a time. This requires solving a simple (shallow) dictionary learning problem, the solution to this is well known. We apply the proposed technique on some benchmark deep learning datasets. We compare our results with other deep learning tools like stacked autoencoder and deep belief network; and state of the art supervised dictionary learning tools like discriminative KSVD and label consistent KSVD. Our method yields better results than all.

The Kaczmarz algorithm is popular for iteratively solving an overdetermined system of linear equations. The traditional Kaczmarz algorithm can approximate the solution in few sweeps through the equations but a randomized version of the Kaczmarz algorithm was shown to converge exponentially and independent of number of equations. Recently an algorithm for finding sparse solution to a linear system of equations has been proposed based on weighted randomized Kaczmarz algorithm. These algorithms solves single measurement vector problem; however there are applications were multiple-measurements are available. In this work, the objective is to solve a multiple measurement vector problem with common sparse support by modifying the randomized Kaczmarz algorithm. We have also modeled the problem of face recognition from video as the multiple measurement vector problem and solved using our proposed technique. We have compared the proposed algorithm with state-of-art spectral projected gradient algorithm for multiple measurement vectors on both real and synthetic datasets. The Monte Carlo simulations confirms that our proposed algorithm have better recovery and convergence rate than the MMV version of spectral projected gradient algorithm under fairness constraints.