A Latin square is an $n \times n$ matrix filled with $n$ distinct symbols, each of which appears exactly once in each row and exactly once in each column. We introduce a problem of allocating $n$ indivisible items among $n$ agents over $n$ rounds while satisfying the Latin square constraint. This constraint ensures that each agent receives no more than one item per round and receives each item at most once. Each agent has an additive valuation on the item--round pairs. Real-world applications like scheduling, resource management, and experimental design require the Latin square constraint to satisfy fairness or balancedness in allocation. Our goal is to find a partial or complete allocation that maximizes the sum of the agents' valuations (utilitarian social welfare) or the minimum of the agents' valuations (egalitarian social welfare). For the problem of maximizing utilitarian social welfare, we prove NP-hardness even when the valuations are binary additive. We then provide $(1-1/e)$ and $(1-1/e)/4$-approximation algorithms for partial and complete settings, respectively. Additionally, we present fixed-parameter tractable (FPT) algorithms with respect to the order of Latin square and the optimum value for both partial and complete settings. For the problem of maximizing egalitarian social welfare, we establish that deciding whether the optimum value is at most $1$ or at least $2$ is NP-hard for both the partial and complete settings, even when the valuations are binary. Furthermore, we demonstrate that checking the existence of a complete allocation that satisfies each of envy-free, proportional, equitable, envy-free up to any good, proportional up to any good, or equitable up to any good is NP-hard, even when the valuations are identical.

Value-alignment in normative multi-agent systems is used to promote a certain value and to ensure the consistent behavior of agents in autonomous intelligent systems with human values. However, the current literature is limited to incorporation of effective norms for single value alignment with no consideration of agents' heterogeneity and the requirement of simultaneous promotion and alignment of multiple values. This research proposes a multi-value promotion model that uses multi-objective evolutionary algorithms to produce the optimum parametric set of norms that is aligned with multiple simultaneous values of heterogeneous agents and the system. To understand various aspects of this complex problem, several evolutionary algorithms were used to find a set of optimised norm parameters considering two toy tax scenarios with two and five values are considered. The results are analysed from different perspectives to show the impact of a selected evolutionary algorithm on the solution, and the importance of understanding the relation between values when prioritising them.

Twitter is a microblogging service for sending short, public text messages (tweets) that has recently received more attention in scientific community. In the works of Sasaki et al. (2010) and Earle et al. (2011) the authors explored the real-time interaction on Twitter for detecting natural hazards (e.g., earthquakes, typhoons) based on the user's tweets on twitter. An inherent challenge for such an application is the natural language processing (NLP), which basically consists in converting the words in numbers (vectors and tensors) in order to (mathematically/ computationally) make predictions and classifications. Recently advanced computational tools have been made available for dealing with text computationally. In this report were implemented a NLP machine learning with TensorFlow, an end-to-end open source platform for machine learning, to process and classify events based on files containing only text.

As we discussed previously, Machine Learning refers to algorithms that are used to identify patterns within data. But what exactly do we mean by "patterns", what all can we do with ML, and what is all this jargon about "models" and "training" them. In this article, I'll try to explain all this without getting too technical, and what you, as a business-user, should know about Machine Learning. Supervised Learning implies use-cases where we have a target we're trying to predict given the data. Supervised algorithms enable us to predict the target (for example the estimated credit limit, tractor sales, if the customer will churn, or the mail category) using the input data (customer's credit history, weather and macroeconomic conditions, customer's activity on the platform, mail specifications). There are models both for Regression and Classification problems, i.e. algorithms which can solve these types of problems.

In machine learning, one of the frequently encountered problems is grouping similar data together. You know the income level of people and now you want to group people with similar income levels together. You want to know who are the people with low income power, the people with high or very high income power, which you think can be helpful in devising a perfect marketing strategy. You have the shopping data of customers with you and now you want to group customers with similar shopping preferences together or you being the bio student want to know which cells share similar properties based upon the data about the cells you have at your hand. All the above stated problems come under the domain of an unsupervised machine learning method called clustering. Although there are a number of clustering algorithms there but when it comes to the simplest one, the award will go to K-Means clustering.

Least mean squares (LMS) is a particular case of the backpropagation (BP) algorithm applied to single-layer neural networks with the mean squared error (MSE) loss. One drawback of the LMS is that the instantaneous weight update is proportional to the square of the norm of the input vector. Normalized least mean squares (NLMS) algorithm amends this drawback by dividing the weight changes by the square of the norm of the input vector. The affine projection algorithm (APA) improved the NLMS algorithm to weight update over a batch of recently seen samples. However, the application of NLMS and APA had been limited to single-layer networks and adaptive filters. In this paper, we consider a virtual target for each neuron of a multi-layer neural network and show that the BP algorithm is equivalent to training the weights of each layer using these virtual targets and the LMS algorithm. We also introduce a consequentialism interpretation of the NLMS and the APA algorithms that justifies their use in multi-layer neural networks. Given any optimization algorithm based on the BP over mini-batches, we propose a novel consequentialism method for updating the weights.Consequently, our proposed weight update can be applied both to plain stochastic gradient descent (SGD) and to momentum methods like RMSProp, Adam, and NAG. These ideas helped us to update the weights more carefully in such a way that minimization of the loss for one sample of the mini-batch does not interfere with other samples in that mini-batch. Our experiments show the usefulness of the proposed method in optimizing deep neural network architectures.

Bayesian optimization has demonstrated impressive success in finding the optimum location $x^{*}$ and value $f^{*}=f(x^{*})=\max_{x\in\mathcal{X}}f(x)$ of the black-box function $f$. In some applications, however, the optimum value is known in advance and the goal is to find the corresponding optimum location. Existing work in Bayesian optimization (BO) has not effectively exploited the knowledge of $f^{*}$ for optimization. In this paper, we consider a new setting in BO in which the knowledge of the optimum value is available. Our goal is to exploit the knowledge about $f^{*}$ to search for the location $x^{*}$ efficiently. To achieve this goal, we first transform the Gaussian process surrogate using the information about the optimum value. Then, we propose two acquisition functions, called confidence bound minimization and expected regret minimization, which exploit the knowledge about the optimum value to identify the optimum location efficiently. We show that our approaches work both intuitively and quantitatively achieve better performance against standard BO methods. We demonstrate real applications in tuning a deep reinforcement learning algorithm on the CartPole problem and XGBoost on Skin Segmentation dataset in which the optimum values are publicly available.

If you have been using GBM as a'black box' till now, may be it's time for you to open it and see, how it actually works! This article is inspired by Owen Zhang's (Chief Product Officer at DataRobot and Kaggle Rank 3) approach shared at NYC Data Science Academy. He delivered a 2 hours talk and I intend to condense it and present the most precious nuggets here. Boosting algorithms play a crucial role in dealing with bias variance trade-off. Unlike bagging algorithms, which only controls for high variance in a model, boosting controls both the aspects (bias & variance), and is considered to be more effective.

XGBoost algorithm has become the ultimate weapon of many data scientist. It's a highly sophisticated algorithm, powerful enough to deal with all sorts of irregularities of data. Building a model using XGBoost is easy. But, improving the model using XGBoost is difficult (at least I struggled a lot). This algorithm uses multiple parameters.

If you have been using GBM as a'black box' till now, may be it's time for you to open it and see, how it actually works! This article is inspired by Owen Zhang's (Chief Product Officer at DataRobot and Kaggle Rank 3) approach shared at NYC Data Science Academy. He delivered a 2 hours talk and I intend to condense it and present the most precious nuggets here. Boosting algorithms play a crucial role in dealing with bias variance trade-off. Unlike bagging algorithms, which only controls for high variance in a model, boosting controls both the aspects (bias & variance), and is considered to be more effective.