Tomas McKelvey

Tomas McKelvey

A regression model with more parameters than data points in the training data is overparametrized and has the capability to interpolate the training data. Based on the classical bias-variance tradeoff expressions, it is commonly assumed that models which interpolate noisy training data are poor to generalize. In some cases, this is not true. The best models obtained are overparametrized and the testing error exhibits the double descent behavior as the model order increases. In this contribution, we provide some analysis to explain the double descent phenomenon, first reported in the machine learning literature. We focus on interpolating models derived from the minimum norm solution to the classical least-squares problem and also briefly discuss model fitting using ridge regression. We derive a result based on the behavior of the smallest singular value of the regression matrix that explains the peak location and the double descent shape of the testing error as a function of model order.

Yinan Yu, Samuel Scheidegger, Tomas McKelvey

Deep Convolutional Neural Networks (CNNs) have been widely used in various domains due to their impressive capabilities. These models are typically composed of a large number of 2D convolutional (Conv2D) layers with numerous trainable parameters. To reduce the complexity of a network, compression techniques can be applied. These methods typically rely on the analysis of trained deep learning models. However, in some applications, due to reasons such as particular data or system specifications and licensing restrictions, a pre-trained network may not be available. This would require the user to train a CNN from scratch. In this paper, we aim to find an alternative parameterization to Conv2D filters without relying on a pre-trained convolutional network. During the analysis, we observe that the effective rank of the vectorized Conv2D filters decreases with respect to the increasing depth in the network, which then leads to the implementation of the Depthwise Convolutional Eigen-Filter (DeCEF) layer. Essentially, a DeCEF layer is a low rank version of the Conv2D layer with significantly fewer trainable parameters and floating point operations (FLOPs). The way we define the effective rank is different from the previous work and it is easy to implement in any deep learning frameworks. To evaluate the effectiveness of DeCEF, experiments are conducted on the benchmark datasets CIFAR-10 and ImageNet using various network architectures. The results have shown a similar or higher accuracy and robustness using about 2/3 of the original parameters and reducing the number of FLOPs to 2/3 of the base network, which is then compared to the state-of-the-art techniques.

Yinan Yu, Tomas McKelvey

Metric learning for classification has been intensively studied over the last decade. The idea is to learn a metric space induced from a normed vector space on which data from different classes are well separated. Different measures of the separation thus lead to various designs of the objective function in the metric learning model. One classical metric is the Mahalanobis distance, where a linear transformation matrix is designed and applied on the original dataset to obtain a new subspace equipped with the Euclidean norm. The kernelized version has also been developed, followed by Multiple-Kernel learning models. In this paper, we consider metric learning to be the identification of the best kernel function with respect to a high class separability in the corresponding metric space. The contribution is twofold: 1) No pairwise computations are required as in most metric learning techniques; 2) Better flexibility and lower computational complexity is achieved using the CLAss-Specific (Multiple) Kernel - Metric Learning (CLAS(M)K-ML). The proposed techniques can be considered as a preprocessing step to any kernel method or kernel approximation technique. An extension to a hierarchical learning structure is also proposed to further improve the classification performance, where on each layer, the CLASMK is computed based on a selected "marginal" subset and feature vectors are constructed by concatenating the features from all previous layers.