Machine learning is a subset of artificial intelligence that involves the use of algorithms and statistical models to enable computers to improve their performance on a specific task through experience. It is an increasingly important field with a wide range of applications, from image and speech recognition to natural language processing and decision-making. So, nowadays we can do anything using machine learning as long as we have data available for the job at hand. One of the key advantages of machine learning is its ability to automatically improve and adapt to new data. This allows it to be used in dynamic and complex systems, such as in healthcare, finance, and transportation, where traditional rule-based systems may not be sufficient.

XGBoost, LightGBM, or CatBoost are libraries that share (by default) the same kind of underlying model: decision trees. These decision trees are combined iteratively, using Gradient Boosting. I.e. the addition of new nodes to the current tree is done so that a non-linear objective, usually the squared error, is optimized. To handle the non-linearity, the objective is linearized using its Gradient and Hessian. As a reminder, the prediction process is relatively simple: given a row of data, each decision tree of the ensemble is browsed.

Linear/Logistic Regression: a statistical method for modeling the linear relationship between a dependent variable and one or more independent variables -- can be used to understand the relationships between variables based on the t-tests and coefficients. Decision Trees: a type of machine learning algorithm that creates a tree-like model of decisions and their possible consequences. They are useful for understanding the relationships between variables by looking at the rules that split the branches. Principal Component Analysis (PCA): a dimensionality reduction technique that projects the data onto a lower-dimensional space while retaining as much variance as possible. PCA can be used to simplify the data or to determine feature importance.

We present a novel quantum algorithm for estimating Gibbs partition functions in sublinear time with respect to the logarithm of the size of the state space. This is the first speed-up of this type to be obtained over the seminal nearly-linear time algorithm of \v{S}tefankovi\v{c}, Vempala and Vigoda [JACM, 2009]. Our result also preserves the quadratic speed-up in precision and spectral gap achieved in previous work by exploiting the properties of quantum Markov chains. As an application, we obtain new polynomial improvements over the best-known algorithms for computing the partition function of the Ising model, counting the number of $k$-colorings, matchings or independent sets of a graph, and estimating the volume of a convex body. Our approach relies on developing new variants of the quantum phase and amplitude estimation algorithms that return nearly unbiased estimates with low variance and without destroying their initial quantum state. We extend these subroutines into a nearly unbiased quantum mean estimator that reduces the variance quadratically faster than the classical empirical mean. No such estimator was known to exist prior to our work. These properties, which are of general interest, lead to better convergence guarantees within the paradigm of simulated annealing for computing partition functions.

Phosphorescent metal complexes have been under intense investigations as emissive dopants for energy efficient organic light emitting diodes (OLEDs). Among them, cyclometalated Pt(II) complexes are widespread triplet emitters with color-tunable emissions. To render their practical applications as OLED emitters, it is in great need to develop Pt(II) complexes with high radiative decay rate constant ($k_r$) and photoluminescence (PL) quantum yield. Thus, an efficient and accurate prediction tool is highly desirable. Here, we develop a general protocol for accurate predictions of emission wavelength, radiative decay rate constant, and PL quantum yield for phosphorescent Pt(II) emitters based on the combination of first-principles quantum mechanical method, machine learning (ML) and experimental calibration. A new dataset concerning phosphorescent Pt(II) emitters is constructed, with more than two hundred samples collected from the literature. Features containing pertinent electronic properties of the complexes are chosen. Our results demonstrate that ensemble learning models combined with stacking-based approaches exhibit the best performance, where the values of squared correlation coefficients ($R^2$), mean absolute error (MAE), and root mean square error (RMSE) are 0.96, 7.21 nm and 13.00 nm for emission wavelength prediction, and 0.81, 0.11 and 0.15 for PL quantum yield prediction. For radiative decay rate constant ($k_r$), the obtained value of $R^2$ is 0.67 while MAE and RMSE are 0.21 and 0.25 (both in log scale), respectively. The accuracy of the protocol is further confirmed using 24 recently reported Pt(II) complexes, which demonstrates its reliability for a broad palette of Pt(II) emitters.We expect this protocol will become a valuable tool, accelerating the rational design of novel OLED materials with desired properties.

We present a non-asymptotic lower bound on the eigenspectrum of the design matrix generated by any linear bandit algorithm with sub-linear regret when the action set has well-behaved curvature. Specifically, we show that the minimum eigenvalue of the expected design matrix grows as $\Omega(\sqrt{n})$ whenever the expected cumulative regret of the algorithm is $O(\sqrt{n})$, where $n$ is the learning horizon, and the action-space has a constant Hessian around the optimal arm. This shows that such action-spaces force a polynomial lower bound rather than a logarithmic lower bound, as shown by \cite{lattimore2017end}, in discrete (i.e., well-separated) action spaces. Furthermore, while the previous result is shown to hold only in the asymptotic regime (as $n \to \infty$), our result for these "locally rich" action spaces is any-time. Additionally, under a mild technical assumption, we obtain a similar lower bound on the minimum eigen value holding with high probability. We apply our result to two practical scenarios -- \emph{model selection} and \emph{clustering} in linear bandits. For model selection, we show that an epoch-based linear bandit algorithm adapts to the true model complexity at a rate exponential in the number of epochs, by virtue of our novel spectral bound. For clustering, we consider a multi agent framework where we show, by leveraging the spectral result, that no forced exploration is necessary -- the agents can run a linear bandit algorithm and estimate their underlying parameters at once, and hence incur a low regret.

In the big-data age, tabular data are being generated and analyzed everywhere. As a consequence, finding and understanding the relationships between the features in these data are of great relevance. Here, to encompass these relationships, we propose a graph-based method that allows individual, group and multi-scale analyses. The method starts by mapping the tabular data into a weighted directed graph using the Shapley additive explanations technique. With this graph of relationships, we show that the inference of the hierarchical modular structure obtained by the Nested Stochastic Block Model (nSBM) as well as the study of the spectral space of the magnetic Laplacian can help us identify the classes of features and unravel non-trivial relationships. As a case study, we analyzed a socioeconomic survey conducted with students in Brazil: the PeNSE survey. The spectral embedding of the columns suggested that questions related to physical activities form a separate group. The application of the nSBM approach not only corroborated with that but allowed complementary findings about the modular structure: some groups of questions showed a high adherence with the divisions qualitatively defined by the designers of the survey. As opposed to the structure obtained by the spectrum, questions from the class Safety were partly grouped by our method in the class Drugs. Surprisingly, by inspecting these questions, we observed that they were related to both these topics, suggesting an alternative interpretation of these questions. These results show how our method can provide guidance for tabular data analysis as well as the design of future surveys.

Langevin algorithms are gradient descent methods augmented with additive noise, and are widely used in Markov Chain Monte Carlo (MCMC) sampling, optimization, and machine learning. In recent years, the non-asymptotic analysis of Langevin algorithms for non-convex learning has been extensively explored. For constrained problems with non-convex losses over a compact convex domain with IID data variables, the projected Langevin algorithm achieves a deviation of $O(T^{-1/4} (\log T)^{1/2})$ from its target distribution [27] in $1$-Wasserstein distance. In this paper, we obtain a deviation of $O(T^{-1/2} \log T)$ in $1$-Wasserstein distance for non-convex losses with $L$-mixing data variables and polyhedral constraints (which are not necessarily bounded). This improves on the previous bound for constrained problems and matches the best-known bound for unconstrained problems.

In today's data-driven world, the sensitivity of information has been a significant concern. With this data and additional information on the person's background, one can easily infer an individual's private data. Many differentially private iterative algorithms have been proposed in interactive settings to protect an individual's privacy from these inference attacks. The existing approaches adapt the method to compute differentially private(DP) centroids by iterative Llyod's algorithm and perturbing the centroid with various DP mechanisms. These DP mechanisms do not guarantee convergence of differentially private iterative algorithms and degrade the quality of the cluster. Thus, in this work, we further extend the previous work on 'Differentially Private k-Means Clustering With Convergence Guarantee' by taking it as our baseline. The novelty of our approach is to sub-cluster the clusters and then select the centroid which has a higher probability of moving in the direction of the future centroid. At every Lloyd's step, the centroids are injected with the noise using the exponential DP mechanism. The results of the experiments indicate that our approach outperforms the current state-of-the-art method, i.e., the baseline algorithm, in terms of clustering quality while maintaining the same differential privacy requirements. The clustering quality significantly improved by 4.13 and 2.83 times than baseline for the Wine and Breast_Cancer dataset, respectively.

In mass manufacturing of jewellery, the gross loss is estimated before manufacturing to calculate the wax weight of the pattern that would be investment casted to make multiple identical pieces of jewellery. Machine learning is a technology that is a part of AI which helps create a model with decision-making capabilities based on a large set of user-defined data. In this paper, the authors found a way to use Machine Learning in the jewellery industry to estimate this crucial Gross Loss. Choosing a small data set of manufactured rings and via regression analysis, it was found out that there is a potential of reducing the error in estimation from +-2-3 to +-0.5 using ML Algorithms from historic data and attributes collected from the CAD file during the design phase itself. To evaluate the approach's viability, additional study must be undertaken with a larger data set.