In real-world applications, we can encounter situations when a well-trained model has to be used to predict from a damaged dataset. The damage caused by missing or corrupted values can be either on the level of individual instances or on the level of entire features. Both situations have a negative impact on the usability of the model on such a dataset. This paper focuses on the scenario where entire features are missing which can be understood as a specific case of transfer learning. Our aim is to experimentally research the influence of various imputation methods on the performance of several classification models. The imputation impact is researched on a combination of traditional methods such as k-NN, linear regression, and MICE compared to modern imputation methods such as multi-layer perceptron (MLP) and gradient boosted trees (XGBT). For linear regression, MLP, and XGBT we also propose two approaches to using them for multiple features imputation. The experiments were performed on both real world and artificial datasets with continuous features where different numbers of features, varying from one feature to 50%, were missing. The results show that MICE and linear regression are generally good imputers regardless of the conditions. On the other hand, the performance of MLP and XGBT is strongly dataset dependent. Their performance is the best in some cases, but more often they perform worse than MICE or linear regression.

Clarice Poon, Gabriel Peyr e † November 12, 2019 Abstract A central question in modern machine learning and imaging sciences is to quantify the number of effective parameters of vastly over-parameterized models. The degrees of freedom is a mathematically convenient way to define this number of parameters. Its computation and properties are well understood when dealing with discretized linear models, possibly regularized using sparsity. In this paper, we argue that this way of thinking is plagued when dealing with models having very large parameter spaces. In this case it makes more sense to consider "off-the-grid" approaches, using a continuous parameter space. This type of approach is the one favoured when training multi-layer perceptrons, and is also becoming popular to solve super-resolution problems in imaging. Training these off-the-grid models with a sparsity inducing prior can be achieved by solving a convex optimization problem over the space of measures, which is often called the Beurling Lasso (Blasso), and is the continuous counterpart of the celebrated Lasso parameter selection method. In previous works [41, 19], the degrees of freedom for the Lasso was shown to coincide with the size of the smallest solution support. Our main contribution is a proof of a continuous counterpart to this result for the Blasso. While in dimension d, each of the k nonzero recovered atom in the recovered measure carries over d 1 parameters ( d for the position and 1 for the weight), a surprising implication of our new formula it that the degrees of freedom for these off-the-grid models is in general strictly smaller ( d 1)k . Our findings thus suggest that discretized methods actually vastly overestimate the number of intrinsic continuous degrees of freedom. Our second contribution is a detailed study of the case of sampling Fourier coefficients in 1D, which corresponds to a super-resolution problem. We show that our formula for the degrees of freedom is valid outside of a set of measure zero of observations, which in turn justifies its use to compute an unbiased estimator of the prediction risk using the Stein Unbiased Risk Estimator (SURE). We also report numerical results for both the case of Fourier sampling and the learning of a multilayers perceptron with a single hidden layer.

The growing number of low-power smart devices in the Internet of Things is coupled with the concept of "Edge Computing", that is moving some of the intelligence, especially machine learning, towards the edge of the network. Enabling machine learning algorithms to run on resource-constrained hardware, typically on low-power smart devices, is challenging in terms of hardware (optimized and energy-efficient integrated circuits), algorithmic and firmware implementations. This paper presents FANN-on-MCU, an open-source toolkit built upon the Fast Artificial Neural Network (FANN) library to run lightweight and energy-efficient neural networks on microcontrollers based on both the ARM Cortex-M series and the novel RISC-V-based Parallel Ultra-Low-Power (PULP) platform. The toolkit takes multi-layer perceptrons trained with FANN and generates code targeted at execution on low-power microcontrollers either with a floating-point unit (i.e., ARM Cortex-M4F and M7F) or without (i.e., ARM Cortex M0-M3 or PULP-based processors). This paper also provides an architectural performance evaluation of neural networks on the most popular ARM Cortex-M family and the parallel RISC-V processor called Mr. Wolf. The evaluation includes experimental results for three different applications using a self-sustainable wearable multi-sensor bracelet. Experimental results show a measured latency in the order of only a few microseconds and a power consumption of few milliwatts while keeping the memory requirements below the limitations of the targeted microcontrollers. In particular, the parallel implementation on the octa-core RISC-V platform reaches a speedup of 22x and a 69% reduction in energy consumption with respect to a single-core implementation on Cortex-M4 for continuous real-time classification.

In this post, we will see how to implement the perceptron model using breast cancer data set in python. A perceptron is a fundamental unit of the neural network which takes weighted inputs, process it and capable of performing binary classifications. This is a follow up to my previous post on the Perceptron Model. If you want to skip the theory and jump into code directly click here. In the perceptron model inputs can be real numbers unlike the Boolean inputs in MP Neuron Model.

This project challenges the car racing problem from OpenAI gym environment. The problem is very challenging since it requires computer to finish the continuous control task by learning from pixels. To tackle this challenging problem, we explored two approaches including evolutionary algorithm based genetic multi-layer perceptron and double deep Q-learning network. The result shows that the genetic multi-layer perceptron can converge fast but when training many episodes, double deep Q-learning can get better score. We analyze the result and draw a conclusion that for limited hardware resources, using genetic multi-layer perceptron sometimes can be more efficient.

To reduce human error and prejudice, many high-stakes decisions have been turned over to machine algorithms. However, recent research suggests that this does not remove discrimination, and can perpetuate harmful stereotypes. While algorithms have been developed to improve fairness, they typically face at least one of three shortcomings: they are not interpretable, they lose significant accuracy compared to unbiased equivalents, or they are not transferable across models. To address these issues, we propose a geometric method that removes correlations between data and any number of protected variables. Further, we can control the strength of debi-asing through an adjustable parameter to address the tradeoff between model accuracy and fairness. The resulting features are interpretable and can be used with many popular models, such as linear regression, random forest and multilayer perceptrons. The resulting predictions are found to be more accurate and fair than several comparable fair AI algorithms across a variety of benchmark datasets. Our work shows that debiasing data is a simple and effective solution toward improving fairness.

We develop a statistical mechanical approach based on the replica method to study the solution space of deep neural networks. Specifically we analyze the configuration space of the synaptic weights in a simple feed-forward perceptron network within a Gaussian approximation for two scenarios : a setting with random inputs/outputs and a teacher-student setting. By increasing the strength of constraints, i. e. increasing the number of imposed patterns, successive 2nd order glass transition (random inputs/outputs) or 2nd order crystalline transition (teacher-student setting) take place place layer-by-layer starting next to the inputs/outputs boundaries going deeper into the bulk. For deep enough network the central part of the network remains in the liquid phase. We argue that in systems of finite width, weak bias field remain in the central part and plays the role of a symmetry breaking field which connects the opposite sides of the system. In the setting with random inputs/outputs, the successive glass transitions bring about a hierarchical free-energy landscape with ultra-metricity, which evolves in space: it is most complex close to the boundaries but becomes renormalized into progressively simpler one in deeper layers. These observations provide clues to understand why deep neural networks operate efficiently. Finally we present results of a set of numerical simulations to examine the theoretical predictions.

As you know a perceptron serves as a basic building block for creating a deep neural network therefore, it is quite obvious that we should begin our journey of mastering Deep Learning with perceptron and learn how to implement it using TensorFlow to solve different problems. In case you are completely new to deep learning, I would suggest you to go through the previous blog of this Deep Learning Tutorial series to avoid any confusion. Basically, a problem is said to be linearly separable if you can classify the data set into two categories or classes using a single line. On the contrary, in case of a non-linearly separable problems, the data set contains multiple classes and requires non-linear line for separating them into their respective classes. Let us visualize the difference between the two by plotting the graph of a linearly separable problem and non-linearly problem data set:Since, you all are familiar with AND Gates, I will be using it as an example to explain how a perceptron works as a linear classifier.

One way to recognise an object is to study how the echo has been shaped during the interaction with the target. Wideband sonar allows the study of the energy distribution for a large range of frequencies. The frequency distribution contains information about an object, including its inner structure. This information is a key for automatic recognition. The scattering by a target can be quantitatively described by its Form Function. The Form Function can be calculated based on the data of the initial pulse, reflected pulse and parameters of a medium where the pulse is propagating. In this work spherical objects are classified based on their filler material - water or air. We limit the study to spherical 2 layered targets immersed in water. The Form Function is used as a descriptor and fed into a Neural Network classifier, Multilayer Perceptron (MLP). The performance of the classifier is compared with Support Vector Machine (SVM) and the Form Function descriptor is examined in contrast to the Time and Frequency Representation of the echo.

When samples have internal structure, we often see a mismatch between the objective optimized during training and the model's goal during inference. For example, in sequence-to-sequence modeling we are interested in high-quality translated sentences, but training typically uses maximum likelihood at the word level. Learning to recognize individual faces from group photos, each captioned with the correct but unordered list of people in it, is another example where a mismatch between training and inference objectives occurs. In both cases, the natural training-time loss would involve a combinatorial problem -- dynamic programming-based global sequence alignment and weighted bipartite graph matching, respectively -- but solutions to combinatorial problems are not differentiable with respect to their input parameters, so surrogate, differentiable losses are used instead. Here, we show how to perform gradient descent over combinatorial optimization algorithms that involve continuous parameters, for example edge weights, and can be efficiently expressed as integer, linear, or mixed-integer linear programs. We demonstrate usefulness of gradient descent over combinatorial optimization in sequence-to-sequence modeling using differentiable encoder-decoder architecture with softmax or Gumbel-softmax, and in weakly supervised learning involving a convolutional, residual feed-forward network for image classification.