National Association of Securities Dealers Automated Quotations(NASDAQ) is an American stock exchange based. It is one of the most valuable stock economic indices in the world and is located in New York City \cite{pagano2008quality}. The volatility of the stock market and the influence of economic indicators such as crude oil, gold, and the dollar in the stock market, and NASDAQ shares are also affected and have a volatile and chaotic nature \cite{firouzjaee2022lstm}.In this article, we have examined the effect of oil, dollar, gold, and the volatility of the stock market in the economic market, and then we have also examined the effect of these indicators on NASDAQ stocks. Then we started to analyze the impact of the feedback on the past prices of NASDAQ stocks and its impact on the current price. Using PCA and Linear Regression algorithm, we have designed an optimal dynamic learning experience for modeling these stocks. The results obtained from the quantitative analysis are consistent with the results of the qualitative analysis of economic studies, and the modeling done with the optimal dynamic experience of machine learning justifies the current price of NASDAQ shares.

Large machine learning models with improved predictions have become widely available in the chemical sciences. Unfortunately, these models do not protect the privacy necessary within commercial settings, prohibiting the use of potentially extremely valuable data by others. Encrypting the prediction process can solve this problem by double-blind model evaluation and prohibits the extraction of training or query data. However, contemporary ML models based on fully homomorphic encryption or federated learning are either too expensive for practical use or have to trade higher speed for weaker security. We have implemented secure and computationally feasible encrypted machine learning models using oblivious transfer enabling and secure predictions of molecular quantum properties across chemical compound space. However, we find that encrypted predictions using kernel ridge regression models are a million times more expensive than without encryption. This demonstrates a dire need for a compact machine learning model architecture, including molecular representation and kernel matrix size, that minimizes model evaluation costs.

This paper analyzes $\ell_1$ regularized linear regression under the challenging scenario of having only adversarially corrupted data for training. We use the primal-dual witness paradigm to provide provable performance guarantees for the support of the estimated regression parameter vector to match the actual parameter. Our theoretical analysis shows the counter-intuitive result that an adversary can influence sample complexity by corrupting the irrelevant features, i.e., those corresponding to zero coefficients of the regression parameter vector, which, consequently, do not affect the dependent variable. As any adversarially robust algorithm has its limitations, our theoretical analysis identifies the regimes under which the learning algorithm and adversary can dominate over each other. It helps us to analyze these fundamental limits and address critical scientific questions of which parameters (like mutual incoherence, the maximum and minimum eigenvalue of the covariance matrix, and the budget of adversarial perturbation) play a role in the high or low probability of success of the LASSO algorithm. Also, the derived sample complexity is logarithmic with respect to the size of the regression parameter vector, and our theoretical claims are validated by empirical analysis on synthetic and real-world datasets.

In this work, we propose a robust framework that employs adversarially robust training to safeguard the machine learning models against perturbed testing data. We achieve this by incorporating the worst-case additive adversarial error within a fixed budget for each sample during model estimation. Our main focus is to provide a plug-and-play solution that can be incorporated in the existing machine learning algorithms with minimal changes. To that end, we derive the ready-to-use solution for several widely used loss functions with a variety of norm constraints on adversarial perturbation for various supervised and unsupervised ML problems, including regression, classification, two-layer neural networks, graphical models, and matrix completion. The solutions are either in closed-form, 1-D optimization, semidefinite programming, difference of convex programming or a sorting-based algorithm. Finally, we validate our approach by showing significant performance improvement on real-world datasets for supervised problems such as regression and classification, as well as for unsupervised problems such as matrix completion and learning graphical models, with very little computational overhead.

Algorithmic stability is a concept from learning theory that expresses the degree to which changes to the input data (e.g., removal of a single data point) may affect the outputs of a regression algorithm. Knowing an algorithm's stability properties is often useful for many downstream applications -- for example, stability is known to lead to desirable generalization properties and predictive inference guarantees. However, many modern algorithms currently used in practice are too complex for a theoretical analysis of their stability properties, and thus we can only attempt to establish these properties through an empirical exploration of the algorithm's behavior on various data sets. In this work, we lay out a formal statistical framework for this kind of "black-box testing" without any assumptions on the algorithm or the data distribution and establish fundamental bounds on the ability of any black-box test to identify algorithmic stability.

Candidate axiom scoring is the task of assessing the acceptability of a candidate axiom against the evidence provided by known facts or data. The ability to score candidate axioms reliably is required for automated schema or ontology induction, but it can also be valuable for ontology and/or knowledge graph validation. Accurate axiom scoring heuristics are often computationally expensive, which is an issue if you wish to use them in iterative search techniques like level-wise generate-and-test or evolutionary algorithms, which require scoring a large number of candidate axioms. We address the problem of developing a predictive model as a substitute for reasoning that predicts the possibility score of candidate class axioms and is quick enough to be employed in such situations. We use a semantic similarity measure taken from an ontology's subsumption structure for this purpose. We show that the approach provided in this work can accurately learn the possibility scores of candidate OWL class axioms and that it can do so for a variety of OWL class axioms.

Algorithms that involve both forecasting and optimization are at the core of solutions to many difficult real-world problems, such as in supply chains (inventory optimization), traffic, and in the transition towards carbon-free energy generation in battery/load/production scheduling in sustainable energy systems. Typically, in these scenarios we want to solve an optimization problem that depends on unknown future values, which therefore need to be forecast. As both forecasting and optimization are difficult problems in their own right, relatively few research has been done in this area. This paper presents the findings of the ``IEEE-CIS Technical Challenge on Predict+Optimize for Renewable Energy Scheduling," held in 2021. We present a comparison and evaluation of the seven highest-ranked solutions in the competition, to provide researchers with a benchmark problem and to establish the state of the art for this benchmark, with the aim to foster and facilitate research in this area. The competition used data from the Monash Microgrid, as well as weather data and energy market data. It then focused on two main challenges: forecasting renewable energy production and demand, and obtaining an optimal schedule for the activities (lectures) and on-site batteries that lead to the lowest cost of energy. The most accurate forecasts were obtained by gradient-boosted tree and random forest models, and optimization was mostly performed using mixed integer linear and quadratic programming. The winning method predicted different scenarios and optimized over all scenarios jointly using a sample average approximation method.

The estimation of cumulative distribution functions (CDFs) is an important learning task with a great variety of downstream applications, such as risk assessments in predictions and decision making. In this paper, we study functional regression of contextual CDFs where each data point is sampled from a linear combination of context dependent CDF basis functions. We propose functional ridge-regression-based estimation methods that estimate CDFs accurately everywhere. In particular, given $n$ samples with $d$ basis functions, we show estimation error upper bounds of $\widetilde{O}(\sqrt{d/n})$ for fixed design, random design, and adversarial context cases. We also derive matching information theoretic lower bounds, establishing minimax optimality for CDF functional regression. Furthermore, we remove the burn-in time in the random design setting using an alternative penalized estimator. Then, we consider agnostic settings where there is a mismatch in the data generation process. We characterize the error of the proposed estimators in terms of the mismatched error, and show that the estimators are well-behaved under model mismatch. Finally, to complete our study, we formalize infinite dimensional models where the parameter space is an infinite dimensional Hilbert space, and establish self-normalized estimation error upper bounds for this setting.

We consider the problem of dynamic pricing of a product in the presence of feature-dependent price sensitivity. Developing practical algorithms that can estimate price elasticities robustly, especially when information about no purchases (losses) is not available, to drive such automated pricing systems is a challenge faced by many industries. Based on the Poisson semi-parametric approach, we construct a flexible yet interpretable demand model where the price related part is parametric while the remaining (nuisance) part of the model is non-parametric and can be modeled via sophisticated machine learning (ML) techniques. The estimation of price-sensitivity parameters of this model via direct one-stage regression techniques may lead to biased estimates due to regularization. To address this concern, we propose a two-stage estimation methodology which makes the estimation of the price-sensitivity parameters robust to biases in the estimators of the nuisance parameters of the model. In the first-stage we construct estimators of observed purchases and prices given the feature vector using sophisticated ML estimators such as deep neural networks. Utilizing the estimators from the first-stage, in the second-stage we leverage a Bayesian dynamic generalized linear model to estimate the price-sensitivity parameters. We test the performance of the proposed estimation schemes on simulated and real sales transaction data from the Airline industry. Our numerical studies demonstrate that our proposed two-stage approach reduces the estimation error in price-sensitivity parameters from 25\% to 4\% in realistic simulation settings. The two-stage estimation techniques proposed in this work allows practitioners to leverage modern ML techniques to robustly estimate price-sensitivities while still maintaining interpretability and allowing ease of validation of its various constituent parts.

The application of machine learning to predicting the properties of small and large discrete (single) molecules and complex materials (polymeric, extended or mixtures of molecules) has been increasing exponentially over the past few decades. Unlike physics-based and rule-based computational systems, machine learning algorithms can learn complex relationships between physicochemical and process parameters and their useful properties for an extremely diverse range of molecular entities. Both the breadth of machine learning methods and the range of physical, chemical, materials, biological, medical and many other application areas have increased markedly in the past decade. This Account summarises three decades of research into improved cheminformatics and machine learning methods and their application to drug design, regenerative medicine, biomaterials, porous and 2D materials, catalysts, biomarkers, surface science, physicochemical and phase properties, nanomaterials, electrical and optical properties, corrosion and battery research. Science has always been fascinated by change, uncovering new aspects of Nature and finding useful ways to exploit them to meet global challenges. The rate of change is accelerating, with average time between innovations decreasing exponentially (Figure 1). Computational molecular design prior to 1990 was focused on the use of computationally expensive physics-based methods like molecular modelling, molecular mechanics, molecular dynamics and quantum chemistry. The quantitative structure–activity relationship (QSAR) methods, developed by Hansch and Fujita in the 1960s, were based on the observation that changes in the constitution of small organic molecules generated a corresponding change in their biological activities. Regression methods were used to find relationships between structure, encoded by mathematical entities called descriptors or features, and biological properties of small organic molecules, also numerically encoded. QSAR use was limited to modelling of small data sets of molecules with similar scaffolds, with the primary aim of understanding the molecular basis for drug (or agrochemical) action. As they were not mechanism- or physics-based, their empirical nature created doubt as to their efficacy, the question of when correlation means causation (still an important issue), and lack of data were major barriers to their wider adoption. After that time, technological developments involving automation, computational power, algorithms, synthesis and informatics have maintained this exponential acceleration.