This paper concerns differentially private Bayesian estimation of the parameters of a population distribution, when a statistic of a sample from that population is shared in noise to provide differential privacy. This work mainly addresses two problems: (1) What statistic of the sample should be shared privately? For the first question, i.e., the one about statistic selection, we promote using the Fisher information. We find out that, the statistic that is most informative in a non-privacy setting may not be the optimal choice under the privacy restrictions. We provide several examples to support that point. We consider several types of data sharing settings and propose several Monte Carlo-based numerical estimation methods for calculating the Fisher information for those settings. The second question concerns inference: (2) Based on the shared statistics, how could we perform effective Bayesian inference? We propose several Markov chain Monte Carlo (MCMC) algorithms for sampling from the posterior distribution of the parameter given the noisy statistic. The proposed MCMC algorithms can be preferred over one another depending on the problem. For example, when the shared statistics is additive and added Gaussian noise, a simple Metropolis-Hasting algorithm that utilizes the central limit theorem is a decent choice. We propose more advanced MCMC algorithms for several other cases of practical relevance. Our numerical examples involve comparing several candidate statistics to be shared privately. For each statistic, we perform Bayesian estimation based on the posterior distribution conditional on the privatized version of that statistic. We demonstrate that, the relative performance of a statistic, in terms of the mean squared error of the Bayesian estimator based on the corresponding privatized statistic, is adequately predicted by the Fisher information of the privatized statistic.

In this paper we provide the quantum version of the Convex Non-negative Matrix Factorization algorithm (Convex-NMF) by using the D-wave quantum annealer. More precisely, we use D-wave 2000Q to find the low rank approximation of a fixed real-valued matrix X by the product of two non-negative matrices factors W and G such that the Frobenius norm of the difference X-XWG is minimized. In order to solve this optimization problem we proceed in two steps. In the first step we transform the global real optimization problem depending on W,G into two quadratic unconstrained binary optimization problems (QUBO) depending on W and G respectively. In the second step we use an alternative strategy between the two QUBO problems corresponding to W and G to find the global solution. The running of these two QUBO problems on D-wave 2000Q need to use an embedding to the chimera graph of D-wave 2000Q, this embedding is limited by the number of qubits of D-wave 2000Q. We perform a study on the maximum number of real data to be used by our approach on D-wave 2000Q. The proposed study is based on the number of qubits used to represent each real variable. We also tested our approach on D-Wave 2000Q with several randomly generated data sets to prove that our approach is faster than the classical approach and also to prove that it gets the best results.

Large neural networks trained in the overparameterized regime are able to fit noise to zero train error. Recent work (Nakkiran and Bansal, 2020) has empirically observed that such networks behave as "conditional samplers" from the noisy distribution. That is, they replicate the noise in the train data to unseen examples. We give a theoretical framework for studying this conditional sampling behavior in the context of learning theory. We relate the notion of such samplers to knowledge distillation, where a student network imitates the outputs of a teacher on unlabeled data. We show that samplers, while being bad classifiers, can be good teachers. Concretely, we prove that distillation from samplers is guaranteed to produce a student which approximates the Bayes optimal classifier. Finally, we show that some common learning algorithms (e.g., Nearest-Neighbours and Kernel Machines) can generate samplers when applied in the overparameterized regime.

In speaker recognition, where speech segments are mapped to embeddings on the unit hypersphere, two scoring backends are commonly used, namely cosine scoring or PLDA. Both have advantages and disadvantages, depending on the context. Cosine scoring follows naturally from the spherical geometry, but for PLDA the blessing is mixed -- length normalization Gaussianizes the between-speaker distribution, but violates the assumption of a speaker-independent within-speaker distribution. We propose PSDA, an analogue to PLDA that uses Von Mises-Fisher distributions on the hypersphere for both within and between-class distributions. We show how the self-conjugacy of this distribution gives closed-form likelihood-ratio scores, making it a drop-in replacement for PLDA at scoring time. All kinds of trials can be scored, including single-enroll and multi-enroll verification, as well as more complex likelihood-ratios that could be used in clustering and diarization. Learning is done via an EM-algorithm with closed-form updates. We explain the model and present some first experiments.

Federated Learning (FL) is a decentralized machine learning architecture, which leverages a large number of remote devices to learn a joint model with distributed training data. However, the system-heterogeneity is one major challenge in a FL network to achieve robust distributed learning performance, which comes from two aspects: i) device-heterogeneity due to the diverse computational capacity among devices; ii) data-heterogeneity due to the non-identically distributed data across the network. Prior studies addressing the heterogeneous FL issue, e.g., FedProx, lack formalization and it remains an open problem. This work first formalizes the system-heterogeneous FL problem and proposes a new algorithm, called FedLGA, to address this problem by bridging the divergence of local model updates via gradient approximation. To achieve this, FedLGA provides an alternated Hessian estimation method, which only requires extra linear complexity on the aggregator. Theoretically, we show that with a device-heterogeneous ratio $\rho$, FedLGA achieves convergence rates on non-i.i.d. distributed FL training data for the non-convex optimization problems with $\mathcal{O} \left( \frac{(1+\rho)}{\sqrt{ENT}} + \frac{1}{T} \right)$ and $\mathcal{O} \left( \frac{(1+\rho)\sqrt{E}}{\sqrt{TK}} + \frac{1}{T} \right)$ for full and partial device participation respectively, where $E$ is the number of local learning epoch, $T$ is the number of total communication round, $N$ is the total device number and $K$ is the number of selected device in one communication round under partially participation scheme. The results of comprehensive experiments on multiple datasets show that FedLGA outperforms current FL methods against the system-heterogeneity.

Machine learning books are a great resource to pump up your knowledge, and in our experience usually explain things better and deeper than online courses or MOOCs. Once you are comfortable with Python and with Data Analysis using its main libraries, it is time to enter the fantastic world of Machine Learning: Predictive models, applications, algorithms, and much more. There are a lot of books out there that try to teach you Machine Learning; here we have only listed some of the best ones. Before getting into more extensive coding ML books, we wanted to offer a book that is more related towards giving the readers an understanding of the main topics of Machine Learning and artificial intelligence in an elegant, clear, and concise manner. Although there is code and maths in the book, the goal of the 100 Page Machine Learning book by Andriy Burkov is to provide a common ground for any kind of person with an STEM background to meet the wonderful world of Data Science. It covers an amazing variety of topics but not in the depth that might be offered by other books (take into account it is only a little more than 100 pages), but it does so in a simple and clear manner, and it is useful for Machine Learning practitioners as well as for newcomers to the field.

Originally published on Towards AI the World's Leading AI and Technology News and Media Company. If you are building an AI-related product or service, we invite you to consider becoming an AI sponsor. At Towards AI, we help scale AI and technology startups. Let us help you unleash your technology to the masses. Logistic Regression is known for modeling classification problems.

Stay updated on last news about Artificial Intelligence. Check your inbox or spam folder to confirm your subscription.

K-Means Clustering is an unsupervised learning algorithm that is used to solve the clustering problems in machine learning or data science. In this article, I would be giving you a detailed explanation and how this model works. Unsupervised Learning method K-Means Clustering divides the unlabeled dataset into various clusters. K specifies the number of pre-defined clusters that must be produced throughout the process; for example, if K 2, two clusters will be created, and if K 3, three clusters will be created, and so on. It allows us to cluster data into distinct groups and provides a simple technique to determine the categories of groups in an unlabeled dataset without any training. It's a centroid-based approach, which means that each cluster has its own centroid.

Continual learning is an emerging paradigm in machine learning, wherein a model is exposed in an online fashion to data from multiple different distributions (i.e. environments), and is expected to adapt to the distribution change. Precisely, the goal is to perform well in the new environment, while simultaneously retaining the performance on the previous environments (i.e. avoid "catastrophic forgetting") -- without increasing the size of the model. While this setup has enjoyed a lot of attention in the applied community, there hasn't be theoretical work that even formalizes the desired guarantees. In this paper, we propose a framework for continual learning through the framework of feature extraction -- namely, one in which features, as well as a classifier, are being trained with each environment. When the features are linear, we design an efficient gradient-based algorithm $\mathsf{DPGD}$, that is guaranteed to perform well on the current environment, as well as avoid catastrophic forgetting. In the general case, when the features are non-linear, we show such an algorithm cannot exist, whether efficient or not.