In this paper, we propose a communication- and computation-efficient algorithm to solve a convex consensus optimization problem defined over a decentralized network. A remarkable existing algorithm to solve this problem is the alternating direction method of multipliers (ADMM), in which at every iteration every node updates its local variable through combining neighboring variables and solving an optimization subproblem. The proposed algorithm, called as COmmunication-censored Linearized ADMM (COLA), leverages a linearization technique to reduce the iteration-wise computation cost of ADMM and uses a communication-censoring strategy to alleviate the communication cost. To be specific, COLA introduces successive linearization approximations to the local cost functions such that the resultant computation is first-order and light-weight. Since the linearization technique slows down the convergence speed, COLA further adopts the communication-censoring strategy to avoid transmissions of less informative messages. A node is allowed to transmit only if the distance between the current local variable and its previously transmitted one is larger than a censoring threshold. COLA is proven to be convergent when the local cost functions have Lipschitz continuous gradients and the censoring threshold is summable. When the local cost functions are further strongly convex, we establish the linear (sublinear) convergence rate of COLA, given that the censoring threshold linearly (sublinearly) decays to 0. Numerical experiments corroborate with the theoretical findings and demonstrate the satisfactory communication-computation tradeoff of COLA.

Partial multi-label learning (PML), which tackles the problem of learning multi-label prediction models from instances with overcomplete noisy annotations, has recently started gaining attention from the research community. In this paper, we propose a novel adversarial learning model, PML-GAN, under a generalized encoder-decoder framework for partial multi-label learning. The PML-GAN model uses a disambiguation network to identify noisy labels and uses a multi-label prediction network to map the training instances to the disambiguated label vectors, while deploying a generative adversarial network as an inverse mapping from label vectors to data samples in the input feature space. The learning of the overall model corresponds to a minimax adversarial game, which enhances the correspondence of input features with the output labels. Extensive experiments are conducted on multiple datasets, while the proposed model demonstrates the state-of-the-art performance for partial multi-label learning.

In the context of machine learning, a prediction problem exhibits predictive multiplicity if there exist several "good" models that attain identical or near-identical performance (i.e., accuracy, AUC, etc.). In this paper, we study the effects of multiplicity in human-facing applications, such as credit scoring and recidivism prediction. We introduce a specific notion of multiplicity -- predictive multiplicity -- to describe the existence of good models that output conflicting predictions. Unlike existing notions of multiplicity (e.g., the Rashomon effect), predictive multiplicity reflects irreconcilable differences in the predictions of models with comparable performance, and presents new challenges for common practices such as model selection and local explanation. We propose measures to evaluate the predictive multiplicity in classification problems. We present integer programming methods to compute these measures for a given datasets by solving empirical risk minimization problems with discrete constraints. We demonstrate how these tools can inform stakeholders on a large collection of recidivism prediction problems. Our results show that real-world prediction problems often admit many good models that output wildly conflicting predictions, and support the need to report predictive multiplicity in model development.

Gaussian process classification (GPC) provides a flexible and powerful statistical framework describing joint distributions over function space. Conventional GPCs however suffer from (i) poor scalability for big data due to the full kernel matrix, and (ii) intractable inference due to the non-Gaussian likelihoods. Hence, various scalable GPCs have been proposed through (i) the sparse approximation built upon a small inducing set to reduce the time complexity; and (ii) the approximate inference to derive analytical evidence lower bound (ELBO). However, these scalable GPCs equipped with analytical ELBO are limited to specific likelihoods or additional assumptions. In this work, we present a unifying framework which accommodates scalable GPCs using various likelihoods. Analogous to GP regression (GPR), we introduce additive noises to augment the probability space for (i) the GPCs with step, (multinomial) probit and logit likelihoods via the internal variables; and particularly, (ii) the GPC using softmax likelihood via the noise variables themselves. This leads to unified scalable GPCs with analytical ELBO by using variational inference. Empirically, our GPCs showcase better results than state-of-the-art scalable GPCs for extensive binary/multi-class classification tasks with up to two million data points.

The study of the LSE has received considerable attention in statistics as well as machine learning; see [9, 36, 41, 54, 55] for important contributions. LSEs are particularly useful when F is known to satisfy some shape constraints such as monotonicity, convexity, or unimodality. In such cases, the LSEs are tuning parameter-free, can be computed as the solution to convex optimization problems, and are adaptive, i.e., the rate of convergence of the LSE changes depending on the "structure" of f 0 [4, 23, 28, 43, 47]. For example, if F is the class of monotone functions and f 0 is a strictly increasing function then ˆ f converges at an n 1/ 3 rate (i.e., null ˆ f f 0null O p(n 1/ 3)); however, if f 0 0, then ˆ f converges at an n 1/ 2 rate [10, 25, 56]. Tsirelson [50] and van de Geer and Wegkamp [53] have established necessary and sufficient conditions on F and null for consistency of ˆ f . Our goal in this work is to provide some general sufficient conditions on F and null under which the LSE is "rate-optimal"; see discussions after Corollary 2.1 for more details, also see Example 3.1. Our results significantly expand the scenarios under which LSE can be proven to be rate-optimal or "be a safe choice" for the model at hand. Theorem 3.2.5 of [55] implies that the LSE ˆ f defined on F satisfies null ˆ f f 0null O p(r n) for any r n such that E null sup f F: null f f 0null r nnull null G n[2null ( f f 0)( X) (f f 0) 2 (X)]null null null C nr 2 n, (3) where C denotes a constant 1 . In the rest of this paper, we make the convention that the constant C is not necessarily the same on each occurrence.

After the last financial crisis, the interest rates decreased exponentially and venture capital suddenly became an attractive option to achieve high returns. However, in only a decade the market moved so fast, got so mature and saturated, and so many empires have been created, that is now cumbersome to obtain sustainable returns investing in risky early-stage companies. In fact, capital is abundant nowadays and funds have been raised everywhere, while there is no scarcity either in companies of every shape and size. For these reasons, investing has become incredibly competitive and it has never been harder to spot the needle in the haystack that would make you rich. Unfortunately, the toolbox investors currently have available is not robust enough to reduce their risk and help them managing uncertainty in a better way. This is where machine learning can come to aid.

To give you an example of the impact of machine learning, Man group's AHL Dimension programme is a $5.1 billion dollar hedge fund which is partially managed by AI. After it started off, by the year 2015, its machine learning algorithms were contributing more than half of the profits of the fund even though the assets under its management were far less. After reading this blog, you would be able to understand the basic logic behind some popular and incredibly resourceful machine learning algorithms which have been used by the trading community as well as serve as the foundation stone on which you step on to create the best machine learning algorithm. Initially developed in statistics to study the relationship between input and output numerical variables, it was adopted by the machine learning community to make predictions based on the linear regression equation. The mathematical representation of linear regression is a linear equation that combines a specific set of input data (x) to predict the output value (y) for that set of input values.

To give you an example of the impact of machine learning, Man group's AHL Dimension programme is a $5.1 billion dollar hedge fund which is partially managed by AI. After it started off, by the year 2015, its machine learning algorithms were contributing more than half of the profits of the fund even though the assets under its management were far less. After reading this blog, you would be able to understand the basic logic behind some popular and incredibly resourceful machine learning algorithms which have been used by the trading community as well as serve as the foundation stone on which you step on to create the best machine learning algorithm. Initially developed in statistics to study the relationship between input and output numerical variables, it was adopted by the machine learning community to make predictions based on the linear regression equation. The mathematical representation of linear regression is a linear equation that combines a specific set of input data (x) to predict the output value (y) for that set of input values.

The article contains a brief introduction of Bioinformatics and how a machine learning classification algorithm can be used to classify the type of cancer in each patient by their gene expressions. Bioinformatics is a field of study that uses computation to extract knowledge from biological data. It includes the collection, storage, retrieval, manipulation and modeling of data for analysis, visualization or prediction through the development of algorithms and software. We can quote it in a simpler way "Bioinformatics deals with computational and mathematical approaches for understanding and processing biological data". It is an interdisciplinary field in which new computational methods are developed to analyze biological data and to make biological discoveries.

Based on some of our recent research and learnings, here are some of the most common use cases of Artificial Intelligence and Machine Learning techniques used in finance. This link is a good introduction of machine learning. This article is good read for both technical and non technical people. Fraud detection is topic that is applicable to many industries like Banking, Finance, Insurance, Government policies etc. Recent rise in digitization fraud is becoming the major problem that finance and banking institutions faces.