Multiple Kernel Learning(MKL) on Support Vector Machines(SVMs) has been a popular front of research in recent times due to its success in application problems like Object Categorization. This success is due to the fact that MKL has the ability to choose from a variety of feature kernels to identify the optimal kernel combination. But the initial formulation of MKL was only able to select the best of the features and misses out many other informative kernels presented. To overcome this, the Lp norm based formulation was proposed by Kloft et. al. This formulation is capable of choosing a non-sparse set of kernels through a control parameter p. Unfortunately, the parameter p does not have a direct meaning to the number of kernels selected. We have observed that stricter control over the number of kernels selected gives us an edge over these techniques in terms of accuracy of classification and also helps us to fine tune the algorithms to the time requirements at hand. In this work, we propose a Controlled Sparsity Kernel Learning (CSKL) formulation that can strictly control the number of kernels which we wish to select. The CSKL formulation introduces a parameter t which directly corresponds to the number of kernels selected. It is important to note that a search in t space is finite and fast as compared to p. We have also provided an efficient Reduced Gradient Descent based algorithm to solve the CSKL formulation, which is proven to converge. Through our experiments on the Caltech101 Object Categorization dataset, we have also shown that one can achieve better accuracies than the previous formulations through the right choice of t.
Even though the details of sparse and non-sparse solutions have been explored, none of these formulations have explicit control of sparsity for their solutions. As we have demonstrated in the experiments section, strict control of sparsity is highly valuable. Hence we propose a formulation, where we can parametrically control the total number of kernels selected and an efficient reduced gradient descent based algorithm to solve it. We have also experimentally shown that our formulation will be able to better state-of-the-art performance on the Caltech101 @cite_8 dataset for object categorization through strict control of sparsity.
@cite_8
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Summary Variable selection for recovering sparsity in nonadditive and nonparametric models with high-dimensional variables has been challenging. This problem becomes even more difficult due to complications in modeling unknown interaction terms among high-dimensional variables. There is currently no variable selection method to overcome these limitations. Hence, in this article we propose a variable selection approach that is developed by connecting a kernel machine with the nonparametric regression model. The advantages of our approach are that it can: (i) recover the sparsity; (ii) automatically model unknown and complicated interactions; (iii) connect with several existing approaches including linear nonnegative garrote and multiple kernel learning; and (iv) provide flexibility for both additive and nonadditive nonparametric models. Our approach can be viewed as a nonlinear version of a nonnegative garrote method. We model the smoothing function by a Least Squares Kernel Machine (LSKM) and construct the nonnegative garrote objective function as the function of the sparse scale parameters of kernel machine to recover sparsity of input variables whose relevances to the response are measured by the scale parameters. We also provide the asymptotic properties of our approach. We show that sparsistency is satisfied with consistent initial kernel function coefficients under certain conditions. An efficient coordinate descent backfitting algorithm is developed. A resampling procedure for our variable selection methodology is also proposed to improve the power. This paper addresses the problem of sparsity penalized least squares for applications in sparse signal processing, e.g., sparse deconvolution. This paper aims to induce sparsity more strongly than L1 norm regularization, while avoiding non-convex optimization. For this purpose, this paper describes the design and use of non-convex penalty functions (regularizers) constrained so as to ensure the convexity of the total cost function F to be minimized. The method is based on parametric penalty functions, the parameters of which are constrained to ensure convexity of F. It is shown that optimal parameters can be obtained by semidefinite programming (SDP). This maximally sparse convex (MSC) approach yields maximally non-convex sparsity-inducing penalty functions constrained such that the total cost function F is convex. It is demonstrated that iterative MSC (IMSC) can yield solutions substantially more sparse than the standard convex sparsity-inducing approach, i.e., L1 norm minimization. This paper investigates a new learning formulation called dynamic group sparsity. It is a natural extension of the standard sparsity concept in compressive sensing, and is motivated by the observation that in some practical sparse data the nonzero coefficients are often not random but tend to be clustered. Intuitively, better results can be achieved in these cases by reasonably utilizing both clustering and sparsity priors. Motivated by this idea, we have developed a new greedy sparse recovery algorithm, which prunes data residues in the iterative process according to both sparsity and group clustering priors rather than only sparsity as in previous methods. The proposed algorithm can recover stably sparse data with clustering trends using far fewer measurements and computations than current state-of-the-art algorithms with provable guarantees. Moreover, our algorithm can adaptively learn the dynamic group structure and the sparsity number if they are not available in the practical applications. We have applied the algorithm to sparse recovery and background subtraction in videos. Numerous experiments with improved performance over previous methods further validate our theoretical proofs and the effectiveness of the proposed algorithm. Sparsity helps reduce the computational complexity of deep neural networks by skipping zeros. Taking advantage of sparsity is listed as a high priority in next generation DNN accelerators such as TPU. The structure of sparsity, i.e., the granularity of pruning, affects the efficiency of hardware accelerator design as well as the prediction accuracy. Coarse-grained pruning creates regular sparsity patterns, making it more amenable for hardware acceleration but more challenging to maintain the same accuracy. In this paper we quantitatively measure the trade-off between sparsity regularity and prediction accuracy, providing insights in how to maintain accuracy while having more a more structured sparsity pattern. Our experimental results show that coarse-grained pruning can achieve a sparsity ratio similar to unstructured pruning without loss of accuracy. Moreover, due to the index saving effect, coarse-grained pruning is able to obtain a better compression ratio than fine-grained sparsity at the same accuracy threshold. Based on the recent sparse convolutional neural network accelerator (SCNN), our experiments further demonstrate that coarse-grained sparsity saves about 2x the memory references compared to fine-grained sparsity. Since memory reference is more than two orders of magnitude more expensive than arithmetic operations, the regularity of sparse structure leads to more efficient hardware design.