## 1 Introduction  
Age estimation from face images is considered as predicting or classifying the real or the apparent age of a person. Facial image estimation is an important step in a wide range of academic and commercial applications [1]. Recently, finding semantic information from images has gained the attention of the research studies due to the vast number of images, which are added on the internet daily or being stored on personal phones and computers. Facial images provide variety of information about a person, such as personal identity, age, gender, color, ethnicity, head pose, eye gaze, and emotion. Designing a robust age estimation system has many challenges. People do age at different rates and they have different aging patterns that can be affected by genetic factors, social conditions, race,ethnicity, and life style [2]. Some people can look years younger than their chronological age while some can look years older. In most cases, the factors that affect aging are personal and difficult to control [3,4]. There are dissimilarities between aging rates of men and women. Women may put makeup to hide aging marks and may wear accessories, resulting in a younger look [5]. Building an efficient large database containing millions of face images for age estimation is relatively very difficult, since it requires an access to participants' private information and the collected images need to be manually labeled. Age estimation can be used to build real-world applications in biometrics, law enforcement, surveillance, and human-computer interaction (HCI). There are two types of biometric systems that are unimodal and multimodal [6]. In a multimodal biometric system, a combination of several traits is collected and one of the traits in this system is the age [7]. Recently, with the astronomical growth of internet content and the spread of the smart machines, age estimation can be used in law enforcement, surveillance, and control applications. For instance, a person's access to cigarettes or alcohol from vending machines can be restricted based on his/her estimated age. Companies, such as Google [8] and Amazon [9], offer products and services based on customers' personalized experience and surfing history. Information of customers' age can be used as one of the distinctive factors of the customer's profiles. Up until a few years ago, low-level features were extracted in most cases and they were used to represent visual image information to design a model for age estimation. Currently, complex and high-level features can be extracted by using deep neural networks (DNNs) and convolutional neural networks (CNNs) to represent the visual information about one's age. In this paper, two high-level feature sets are extracted by using CNNs. Existing benchmarks for age classification task are relatively small when compared to the other benchmarks that are used for other classification tasks, such as image classification, semantic segmentation, and face recognition. Therefore, in this work, pre-trained CNNs from other image tasks are employed to extract the feature sets for age estimation. We propose a regularization framework that is based on a new cost function for selecting the robust features from the original feature sets by combining the DNN and the \(l2\),\(1\)-norm. The analysis and the proof of the convergence of the new cost function to solve the minimization problem of the DNN and the \(l2\),\(1\)-norm are presented. Efficiency of the selected robust features are studied. The jointly fine-tuned CNNs based on the Softmax and the Sigmoid (JFN-SS) in [10] are used and a new jointly fine-tuned framework based on amplifying the output of two DNNs (JFN-A) is introduced. Several methods have been proposed in the literature to represent the age information from the facial images. One of the early models is the anthropometric model that uses the size and proportions of the human face.