Clustering is a Machine Learning method. It is an unsupervised machine learning task. In which, we draw references from datasets consisting of input data without labelled responses. With a clustering algorithm, we give the algorithm a lot of input data with no labels and let it find any groupings in the data it can. We can use a clustering algorithm to categorize each data point into a specific group.

Today we are talking about gradient descent. Firstly what is gradient descent? Gradient descent is an iterative optimization algorithm used in machine learning to minimize a loss function. The loss function describes how well the model will perform given the current set of parameters (weights and biases), and gradient descent is used to find the best set of parameters. We use gradient descent to update the parameters of our model.

What is the one machine learning algorithm -- if you ask -- that consistently gives superior performance in regression and classification? It is arguably the most powerful algorithm and is increasingly being used in all industries and in all problem domains --from customer analytics and sales prediction to fraud detection and credit approval and more. It is also a winning algorithm in many machine learning competitions. In fact, XGBoost was used in 17 out of 29 data science competitions on the Kaggle platform. Not just in businesses and competitions, XGBoost has been used in scientific experiments such as the Large Hadron Collider (the Higgs Boson machine learning challenge). A key to its performance is its hyperparameters.

In recent years a lot of research has been conducted within the area of causal inference and causal learning. Many methods have been developed to identify the cause-effect pairs in models and have been successfully applied to observational real-world data in order to determine the direction of causal relationships. Many of these methods require simplifying assumptions, such as absence of confounding, cycles, and selection bias. Yet in bivariate situations causal discovery problems remain challenging. One class of such methods, that also allows tackling the bivariate case, is based on Additive Noise Models (ANMs). Unfortunately, one aspect of these methods has not received much attention until now: what is the impact of different noise levels on the ability of these methods to identify the direction of the causal relationship. This work aims to bridge this gap with the help of an empirical study. For this work, we considered bivariate cases, which is the most elementary form of a causal discovery problem where one needs to decide whether X causes Y or Y causes X, given joint distributions of two variables X, Y. Furthermore, two specific methods have been selected, \textit{Regression with Subsequent Independence Test} and \textit{Identification using Conditional Variances}, which have been tested with an exhaustive range of ANMs where the additive noises' levels gradually change from 1% to 10000% of the causes' noise level (the latter remains fixed). Additionally, the experiments in this work consider several different types of distributions as well as linear and non-linear ANMs. The results of the experiments show that these methods can fail to capture the true causal direction for some levels of noise.

Increasing interest in privacy-preserving machine learning has led to new models for synthetic private data generation from undisclosed real data. However, mechanisms of privacy preservation introduce artifacts in the resulting synthetic data that have a significant impact on downstream tasks such as learning predictive models or inference. In particular, bias can affect all analyses as the synthetic data distribution is an inconsistent estimate of the real-data distribution. We propose several bias mitigation strategies using privatized likelihood ratios that have general applicability to differentially private synthetic data generative models. Through large-scale empirical evaluation, we show that bias mitigation provides simple and effective privacy-compliant augmentation for general applications of synthetic data. However, the work highlights that even after bias correction significant challenges remain on the usefulness of synthetic private data generators for tasks such as prediction and inference.

Accurate and interpretable prediction of survey response rates is important from an operational standpoint. The US Census Bureau's well-known ROAM application uses principled statistical models trained on the US Census Planning Database data to identify hard-to-survey areas. An earlier crowdsourcing competition revealed that an ensemble of regression trees led to the best performance in predicting survey response rates; however, the corresponding models could not be adopted for the intended application due to limited interpretability. In this paper, we present new interpretable statistical methods to predict, with high accuracy, response rates in surveys. We study sparse nonparametric additive models with pairwise interactions via $\ell_0$-regularization, as well as hierarchically structured variants that provide enhanced interpretability. Despite strong methodological underpinnings, such models can be computationally challenging -- we present new scalable algorithms for learning these models. We also establish novel non-asymptotic error bounds for the proposed estimators. Experiments based on the US Census Planning Database demonstrate that our methods lead to high-quality predictive models that permit actionable interpretability for different segments of the population. Interestingly, our methods provide significant gains in interpretability without losing in predictive performance to state-of-the-art black-box machine learning methods based on gradient boosting and feedforward neural networks. Our code implementation in python is available at https://github.com/ShibalIbrahim/Additive-Models-with-Structured-Interactions.

Sparse deep neural networks have proven to be efficient for predictive model building in large-scale studies. Although several works have studied theoretical and numerical properties of sparse neural architectures, they have primarily focused on the edge selection. Sparsity through edge selection might be intuitively appealing; however, it does not necessarily reduce the structural complexity of a network. Instead pruning excessive nodes in each layer leads to a structurally sparse network which would have lower computational complexity and memory footprint. We propose a Bayesian sparse solution using spike-and-slab Gaussian priors to allow for node selection during training. The use of spike-and-slab prior alleviates the need of an ad-hoc thresholding rule for pruning redundant nodes from a network. In addition, we adopt a variational Bayes approach to circumvent the computational challenges of traditional Markov Chain Monte Carlo (MCMC) implementation. In the context of node selection, we establish the fundamental result of variational posterior consistency together with the characterization of prior parameters. In contrast to the previous works, our theoretical development relaxes the assumptions of the equal number of nodes and uniform bounds on all network weights, thereby accommodating sparse networks with layer-dependent node structures or coefficient bounds. With a layer-wise characterization of prior inclusion probabilities, we also discuss optimal contraction rates of the variational posterior. Finally, we provide empirical evidence to substantiate that our theoretical work facilitates layer-wise optimal node recovery together with competitive predictive performance.

We summarized both common and novel predictive models used for stock price prediction and combined them with technical indices, fundamental characteristics and text-based sentiment data to predict S&P stock prices. A 66.18% accuracy in S&P 500 index directional prediction and 62.09% accuracy in individual stock directional prediction was achieved by combining different machine learning models such as Random Forest and LSTM together into state-of-the-art ensemble models. The data we use contains weekly historical prices, finance reports, and text information from news items associated with 518 different common stocks issued by current and former S&P 500 large-cap companies, from January 1, 2000 to December 31, 2019. Our study's innovation includes utilizing deep language models to categorize and infer financial news item sentiment; fusing different models containing different combinations of variables and stocks to jointly make predictions; and overcoming the insufficient data problem for machine learning models in time series by using data across different stocks.

This paper identifies a structural property of data distributions that enables deep neural networks to learn hierarchically. We define the "staircase" property for functions over the Boolean hypercube, which posits that high-order Fourier coefficients are reachable from lower-order Fourier coefficients along increasing chains. We prove that functions satisfying this property can be learned in polynomial time using layerwise stochastic coordinate descent on regular neural networks -- a class of network architectures and initializations that have homogeneity properties. Our analysis shows that for such staircase functions and neural networks, the gradient-based algorithm learns high-level features by greedily combining lower-level features along the depth of the network. We further back our theoretical results with experiments showing that staircase functions are also learnable by more standard ResNet architectures with stochastic gradient descent. Both the theoretical and experimental results support the fact that staircase properties have a role to play in understanding the capabilities of gradient-based learning on regular networks, in contrast to general polynomial-size networks that can emulate any SQ or PAC algorithms as recently shown.

Multiclass multilabel classification refers to the task of attributing multiple labels to examples via predictions. Current models formulate a reduction of that multilabel setting into either multiple binary classifications or multiclass classification, allowing for the use of existing loss functions (sigmoid, cross-entropy, logistic, etc.). Empirically, these methods have been reported to achieve good performance on different metrics (F1 score, Recall, Precision, etc.). Theoretically though, the multilabel classification reductions does not accommodate for the prediction of varying numbers of labels per example and the underlying losses are distant estimates of the performance metrics. We propose a loss function, sigmoidF1. It is an approximation of the F1 score that (I) is smooth and tractable for stochastic gradient descent, (II) naturally approximates a multilabel metric, (III) estimates label propensities and label counts. More generally, we show that any confusion matrix metric can be formulated with a smooth surrogate. We evaluate the proposed loss function on different text and image datasets, and with a variety of metrics, to account for the complexity of multilabel classification evaluation. In our experiments, we embed the sigmoidF1 loss in a classification head that is attached to state-of-the-art efficient pretrained neural networks MobileNetV2 and DistilBERT. Our experiments show that sigmoidF1 outperforms other loss functions on four datasets and several metrics. These results show the effectiveness of using inference-time metrics as loss function at training time in general and their potential on non-trivial classification problems like multilabel classification.