We consider the dynamic of gradient descent for learning a two-layer neural network. We assume the input $x\in\mathbb{R}^d$ is drawn from a Gaussian distribution and the label of $x$ satisfies $f^{\star}(x) = a^{\top}|W^{\star}x|$, where $a\in\mathbb{R}^d$ is a nonnegative vector and $W^{\star} \in\mathbb{R}^{d\times d}$ is an orthonormal matrix. We show that an over-parametrized two-layer neural network with ReLU activation, trained by gradient descent from random initialization, can provably learn the ground truth network with population loss at most $o(1/d)$ in polynomial time with polynomial samples. On the other hand, we prove that any kernel method, including Neural Tangent Kernel, with a polynomial number of samples in $d$, has population loss at least $\Omega(1 / d)$.

This paper concerns the problem of 1-bit compressed sensing, where the goal is to estimate a sparse signal from a few of its binary measurements. We study a non-convex sparsity-constrained program and present a novel and concise analysis that moves away from the widely used notion of Gaussian width. We show that with high probability a simple algorithm is guaranteed to produce an accurate approximation to the normalized signal of interest under the $\ell_2$-metric. On top of that, we establish an ensemble of new results that address norm estimation, support recovery, and model misspecification. On the computational side, it is shown that the non-convex program can be solved via one-step hard thresholding which is dramatically efficient in terms of time complexity and memory footprint. On the statistical side, it is shown that our estimator enjoys a near-optimal error rate under standard conditions. The theoretical results are substantiated by numerical experiments.

Machine learning algorithms are used in finance, medicine, and criminal justice, and therefore they can have a deep The advent of machine learning techniques has impact on society. With the recent success of AI applications made it possible to obtain predictive systems that in the private and public domain, legal professionals are now have overturned traditional legal practices. However, interested in artificial intelligence, especially since many rather than leading to systems seeking to startups disrupt the legal market space by seeking to benefit replace humans, the search for the determinants of these new AI techniques (Bex et al., 2017). in a court decision makes it possible to give a However, the arrival of these new techniques has brought better understanding of the decision mechanisms a number of ethical issues. Firstly, machine learning and carried out by the judge. By using a large amount data mining techniques are capable of exploiting personal of court decisions in matters of divorce produced and legal data that are more and more easily accessible on by French jurisdictions and by looking at the variables the Internet, leading to questions about privacy preserving, that allow to allocate an alimony or not, and or even attacks on democracy (Wylie, 2019). Secondly, to define its amount, we seek to identify if there artificial intelligence programs reason in a simplistic way, may be extralegal factors in the decisions taken but the real world is complex, especially in the legal field by the judges. From this perspective, we present which leaves a certain part to the human interpretation of an explainable AI model designed in this purpose the law and characterization of the fact. A machine learning by combining a classification with random forest program has great difficulty in dealing with the unexpected and a regression model, as a complementary tool events that happen in the real world. Intelligent system to existing decision-making scales or guidelines algorithms are black boxes that are impossible to understand, created by practitioners.

In some following posts, I will explore these other methods, such as Random Forest, Support Vector Modeling, and XGboost, to see if we can improve on this customer churn model! In my previous post, we completed a pretty in-depth walk through of the exploratory data analysis process for a customer churn analysis dataset. Our data, sourced from Kaggle, is centered around customer churn, the rate at which a commercial customer will leave the commercial platform that they are currently a (paying) customer, of a telecommunications company, Telco. Now that the EDA process has been complete, and we have a pretty good sense of what our data tells us before processing, we can move on to building a Logistic Regression classification model which will allow for us to predict whether a customer is at risk to churn from Telco's platform. The complete GitHub repository with notebooks and data walkthrough can be found here.

Emotion recognition has a pivotal role in affective computing and in human-computer interaction. The current technological developments lead to increased possibilities of collecting data about the emotional state of a person. In general, human perception regarding the emotion transmitted by a subject is based on vocal and visual information collected in the first seconds of interaction with the subject. As a consequence, the integration of verbal (i.e., speech) and non-verbal (i.e., image) information seems to be the preferred choice in most of the current approaches towards emotion recognition. In this paper, we propose a multimodal fusion technique for emotion recognition based on combining audio-visual modalities from a temporal window with different temporal offsets for each modality. We show that our proposed method outperforms other methods from the literature and human accuracy rating. The experiments are conducted over the open-access multimodal dataset CREMA-D.

The tremendous applications of human activity recognition are surging its span from health monitoring systems to virtual reality applications. Thus, the automatic recognition of daily life activities has become significant for numerous applications. In recent years, many datasets have been proposed to train the machine learning models for efficient monitoring and recognition of human daily living activities. However, the performance of machine learning models in activity recognition is crucially affected when there are incomplete activities in a dataset, i.e., having missing samples in dataset captures. Therefore, in this work, we propose a methodology for extrapolating the missing samples of a dataset to better recognize the human daily living activities. The proposed method efficiently pre-processes the data captures and utilizes the k-Nearest Neighbors (KNN) imputation technique to extrapolate the missing samples in dataset captures. The proposed methodology elegantly extrapolated a similar pattern of activities as they were in the real dataset.

Linear models have shown great effectiveness and flexibility in many fields such as machine learning, signal processing and statistics. They can represent rich spaces of functions while preserving the convexity of the optimization problems where they are used, and are simple to evaluate, differentiate and integrate. However, for modeling non-negative functions, which are crucial for unsupervised learning, density estimation, or non-parametric Bayesian methods, linear models are not applicable directly. Moreover, current state-of-the-art models like generalized linear models either lead to non-convex optimization problems, or cannot be easily integrated. In this paper we provide the first model for non-negative functions which benefits from the same good properties of linear models. In particular, we prove that it admits a representer theorem and provide an efficient dual formulation for convex problems. We study its representation power, showing that the resulting space of functions is strictly richer than that of generalized linear models. Finally we extend the model and the theoretical results to functions with outputs in convex cones. The paper is complemented by an experimental evaluation of the model showing its effectiveness in terms of formulation, algorithmic derivation and practical results on the problems of density estimation, regression with heteroscedastic errors, and multiple quantile regression.

We study the problem of learning efficient algorithms that strongly generalize in the framework of neural program induction. By carefully designing the input / output interfaces of the neural model and through imitation, we are able to learn models that produce correct results for arbitrary input sizes, achieving strong generalization. Moreover, by using reinforcement learning, we optimize for program efficiency metrics, and discover new algorithms that surpass the teacher used in imitation. With this, our approach can learn to outperform custom-written solutions for a variety of problems, as we tested it on sorting, searching in ordered lists and the NP-complete 0/1 knapsack problem, which sets a notable milestone in the field of Neural Program Induction. As highlights, our learned model can perform sorting perfectly on any input data size we tested on, with $O(n log n)$ complexity, whilst outperforming hand-coded algorithms, including quick sort, in number of operations even for list sizes far beyond those seen during training.

Intermediate-Severity (IS) faults present milder symptoms compared to severe faults, and are more difficult to detect and diagnose due to their close resemblance to normal operating conditions. The lack of IS fault examples in the training data can pose severe risks to Fault Detection and Diagnosis (FDD) methods that are built upon Machine Learning (ML) techniques, because these faults can be easily mistaken as normal operating conditions. Ensemble models are widely applied in ML and are considered promising methods for detecting out-of-distribution (OOD) data. We identify common pitfalls in these models through extensive experiments with several popular ensemble models on two real-world datasets. Then, we discuss how to design more effective ensemble models for detecting and diagnosing IS faults.

We study two practically important cases of model based clustering using Gaussian Mixture Models: (1) when there is misspecification and (2) on high dimensional data, in the light of recent advances in Gradient Descent (GD) based optimization using Automatic Differentiation (AD). Our simulation studies show that EM has better clustering performance, measured by Adjusted Rand Index, compared to GD in cases of misspecification, whereas on high dimensional data GD outperforms EM. We observe that both with EM and GD there are many solutions with high likelihood but poor cluster interpretation. To address this problem we design a new penalty term for the likelihood based on the Kullback Leibler divergence between pairs of fitted components. Closed form expressions for the gradients of this penalized likelihood are difficult to derive but AD can be done effortlessly, illustrating the advantage of AD-based optimization. Extensions of this penalty for high dimensional data and for model selection are discussed. Numerical experiments on synthetic and real datasets demonstrate the efficacy of clustering using the proposed penalized likelihood approach.