Machine learning relates to the study, design, and development of the algorithms that give computers the capability to learn without being explicitly programmed. While data mining can be defined as the process by which the unstructured data tries to extract knowledge or unknown interesting patterns. During this processing machine, learning algorithms are used. Converting a (usually continuous) feature into multiple binary features called buckets or bins, typically based on value range. For example, instead of representing temperature as a single continuous floating-point feature, you could chop ranges of temperatures into discrete bins.

We propose a novel appearance-based gesture recognition algorithm using compressed domain signal processing techniques. Gesture features are extracted directly from the compressed measurements, which are the block averages and the coded linear combinations of the image sensor's pixel values. We also improve both the computational efficiency and the memory requirement of the previous DTW-based K-NN gesture classifiers. Both simulation testing and hardware implementation strongly support the proposed algorithm.

In the past decade, sparse principal component analysis has emerged as an archetypal problem for illustrating statistical-computational tradeoffs. This trend has largely been driven by a line of research aiming to characterize the average-case complexity of sparse PCA through reductions from the planted clique (PC) conjecture - which conjectures that there is no polynomial-time algorithm to detect a planted clique of size $K = o(N^{1/2})$ in $\mathcal{G}(N, \frac{1}{2})$. All previous reductions to sparse PCA either fail to show tight computational lower bounds matching existing algorithms or show lower bounds for formulations of sparse PCA other than its canonical generative model, the spiked covariance model. Also, these lower bounds all quickly degrade with the exponent in the PC conjecture. Specifically, when only given the PC conjecture up to $K = o(N^\alpha)$ where $\alpha < 1/2$, there is no sparsity level $k$ at which these lower bounds remain tight. If $\alpha \le 1/3$ these reductions fail to even show the existence of a statistical-computational tradeoff at any sparsity $k$. We give a reduction from PC that yields the first full characterization of the computational barrier in the spiked covariance model, providing tight lower bounds at all sparsities $k$. We also show the surprising result that weaker forms of the PC conjecture up to clique size $K = o(N^\alpha)$ for any given $\alpha \in (0, 1/2]$ imply tight computational lower bounds for sparse PCA at sparsities $k = o(n^{\alpha/3})$. This shows that even a mild improvement in the signal strength needed by the best known polynomial-time sparse PCA algorithms would imply that the hardness threshold for PC is subpolynomial. This is the first instance of a suboptimal hardness assumption implying optimal lower bounds for another problem in unsupervised learning.

Traditional load analysis is facing challenges with the new electricity usage patterns due to demand response as well as increasing deployment of distributed generations, including photovoltaics (PV), electric vehicles (EV), and energy storage systems (ESS). At the transmission system, despite of irregular load behaviors at different areas, highly aggregated load shapes still share similar characteristics. Load clustering is to discover such intrinsic patterns and provide useful information to other load applications, such as load forecasting and load modeling. This paper proposes an efficient submodular load clustering method for transmission-level load areas. Robust principal component analysis (R-PCA) firstly decomposes the annual load profiles into low-rank components and sparse components to extract key features. A novel submodular cluster center selection technique is then applied to determine the optimal cluster centers through constructed similarity graph. Following the selection results, load areas are efficiently assigned to different clusters for further load analysis and applications. Numerical results obtained from PJM load demonstrate the effectiveness of the proposed approach.

In this paper, we consider batch supervised learning where an adversary is allowed to corrupt instances with arbitrarily large noise. The adversary is allowed to corrupt any $l$ features in each instance and the adversary can change their values in any way. This noise is introduced on test instances and the algorithm receives no label feedback for these instances. We provide several subspace voting techniques that can be used to transform existing algorithms and prove data-dependent performance bounds in this setting. The key insight to our results is that we set our parameters so that a significant fraction of the voting hypotheses do not contain corrupt features and, for many real world problems, these uncorrupt hypotheses are sufficient to achieve high accuracy. We empirically validate our approach on several datasets including three new datasets that deal with side channel electromagnetic information.

We present algorithms for efficiently learning regularizers that improve generalization. Our approach is based on the insight that regularizers can be viewed as upper bounds on the generalization gap, and that reducing the slack in the bound can improve performance on test data. For a broad class of regularizers, the hyperparameters that give the best upper bound can be computed using linear programming. Under certain Bayesian assumptions, solving the LP lets us "jump" to the optimal hyperparameters given very limited data. This suggests a natural algorithm for tuning regularization hyperparameters, which we show to be effective on both real and synthetic data.

We consider the problem of learning from sparse and underspecified rewards, where an agent receives a complex input, such as a natural language instruction, and needs to generate a complex response, such as an action sequence, while only receiving binary success-failure feedback. Such success-failure rewards are often underspecified: they do not distinguish between purposeful and accidental success. Generalization from underspecified rewards hinges on discounting spurious trajectories that attain accidental success, while learning from sparse feedback requires effective exploration. We address exploration by using a mode covering direction of KL divergence to collect a diverse set of successful trajectories, followed by a mode seeking KL divergence to train a robust policy. We propose Meta Reward Learning (MeRL) to construct an auxiliary reward function that provides more refined feedback for learning. The parameters of the auxiliary reward function are optimized with respect to the validation performance of a trained policy. The MeRL approach outperforms our alternative reward learning technique based on Bayesian Optimization, and achieves the state-of-the-art on weakly-supervised semantic parsing. It improves previous work by 1.2% and 2.4% on WikiTableQuestions and WikiSQL datasets respectively.

The persistence diagram is an increasingly useful tool arising from the field of Topological Data Analysis. However, using these diagrams in conjunction with machine learning techniques requires some mathematical finesse. The most success to date has come from finding methods for turning persistence diagrams into vectors in $\mathbb{R}^n$ in a way which preserves as much of the space of persistence diagrams as possible, commonly referred to as featurization. In this paper, we describe a mathematical framework for featurizing the persistence diagram space using template functions. These functions are general as they are only required to be continuous, have a compact support, and separate points. We discuss two example realizations of these functions: tent functions and Chybeyshev interpolating polynomials. Both of these functions are defined on a grid superposed on the birth-lifetime plane. We then combine the resulting features with machine learning algorithms to perform supervised classification and regression on several example data sets, including manifold data, shape data, and an embedded time series from a Rossler system. Our results show that the template function approach yields high accuracy rates that match and often exceed the results of existing methods for featurizing persistence diagrams. One counter-intuitive observation is that in most cases using interpolating polynomials, where each point contributes globally to the feature vector, yields significantly better results than using tent functions, where the contribution of each point is localized to its grid cell. Along the way, we also provide a complete characterization of compact sets in persistence diagram space endowed with the bottleneck distance.

Graph Convolutional Networks (GCNs) and their variants have experienced significant attention and have become the de facto methods for learning graph representations. GCNs derive inspiration primarily from recent deep learning approaches, and as a result, may inherit unnecessary complexity and redundant computation. In this paper, we reduce this excess complexity through successively removing nonlinearities and collapsing weight matrices between consecutive layers. We theoretically analyze the resulting linear model and show that it corresponds to a fixed low-pass filter followed by a linear classifier. Notably, our experimental evaluation demonstrates that these simplifications do not negatively impact accuracy in many downstream applications. Moreover, the resulting model scales to larger datasets, is naturally interpretable, and yields up to two orders of magnitude speedup over FastGCN.

Adaptive gradient methods like AdaGrad are widely used in optimizing neural networks. Yet, existing convergence guarantees for adaptive gradient methods require either convexity or smoothness, and, in the smooth setting, only guarantee convergence to a stationary point. We propose an adaptive gradient method and show that for two-layer over-parameterized neural networks -- if the width is sufficiently large (polynomially) -- then the proposed method converges \emph{to the global minimum} in polynomial time, and convergence is robust, \emph{ without the need to fine-tune hyper-parameters such as the step-size schedule and with the level of over-parametrization independent of the training error}. Our analysis indicates in particular that over-parametrization is crucial for the harnessing the full potential of adaptive gradient methods in the setting of neural networks.