Congratulations!, you have just created a Linear Regression Model using Julia's Flux.jl library. Hopefully this blog has helped you to understand the basics of Flux.jl library so that you can create your own personalized ML models from scratch. I am planning to create a series in which this blog is part one of that series. The other parts could include deploying this Regression Model using streamlit/flask and also developing Deep Learning models using the Flux.jl

Variational inference (VI) is a technique to approximate difficult to compute posteriors by optimization. In contrast to MCMC, VI scales to many observations. In the case of complex posteriors, however, state-of-the-art VI approaches often yield unsatisfactory posterior approximations. This paper presents Bernstein flow variational inference (BF-VI), a robust and easy-to-use method, flexible enough to approximate complex multivariate posteriors. BF-VI combines ideas from normalizing flows and Bernstein polynomial-based transformation models. In benchmark experiments, we compare BF-VI solutions with exact posteriors, MCMC solutions, and state-of-the-art VI methods including normalizing flow based VI. We show for low-dimensional models that BF-VI accurately approximates the true posterior; in higher-dimensional models, BF-VI outperforms other VI methods. Further, we develop with BF-VI a Bayesian model for the semi-structured Melanoma challenge data, combining a CNN model part for image data with an interpretable model part for tabular data, and demonstrate for the first time how the use of VI in semi-structured models.

For instance, one would expect certain levels of similarities between the We consider the problem of estimating the topology of multiple networks brain networks of different healthy individuals or between the same from nodal observations, where these networks are assumed social network observed at different points in time. Prominent methods to be drawn from the same (unknown) random graph model. We for multiple network inference include statistical approaches, adopt a graphon as our random graph model, which is a nonparametric primarily consisting of the joint estimation of Gaussian graphical model from which graphs of potentially different sizes can models [13-17]. These methods typically involve modifications on be drawn. The versatility of graphons allows us to tackle the joint the graphical lasso formulation with additional encouragement of inference problem even for the cases where the graphs to be recovered structural similarity. Estimation of time-varying graphs is widely contain different number of nodes and lack precise alignment popular, as the relationship between graphs is typically straightforward across the graphs. Our solution is based on combining a maximum to implement by considering that graph variation is smooth likelihood penalty with graphon estimation schemes and can be used across time [18, 19]. The above methods for estimating multiple networks to augment existing network inference methods. We validate our typically enforce similar structure, such as promoting similar proposed approach by comparing its performance against competing sparsity patterns [20].

The major problem of fitting a higher order Markov model is the exponentially growing number of parameters. The most popular approach is to use a Variable Length Markov Chain (VLMC), which determines relevant contexts (recent pasts) of variable orders and form a context tree. A more general approach is called Sparse Markov Model (SMM), where all possible histories of order $m$ form a partition so that the transition probability vectors are identical for the histories belonging to a particular group. We develop an elegant method of fitting SMM using convex clustering, which involves regularization. The regularization parameter is selected using BIC criterion. Theoretical results demonstrate the model selection consistency of our method for large sample size. Extensive simulation studies under different set-up have been presented to measure the performance of our method. We apply this method to classify genome sequences, obtained from individuals affected by different viruses.

In many practical applications of AI, an AI model is used as a decision aid for human users. The AI provides advice that a human (sometimes) incorporates into their decision-making process. The AI advice is often presented with some measure of "confidence" that the human can use to calibrate how much they depend on or trust the advice. In this paper, we demonstrate that presenting AI models as more confident than they actually are, even when the original AI is well-calibrated, can improve human-AI performance (measured as the accuracy and confidence of the human's final prediction after seeing the AI advice). We first learn a model for how humans incorporate AI advice using data from thousands of human interactions. This enables us to explicitly estimate how to transform the AI's prediction confidence, making the AI uncalibrated, in order to improve the final human prediction. We empirically validate our results across four different tasks -- dealing with images, text and tabular data -- involving hundreds of human participants. We further support our findings with simulation analysis. Our findings suggest the importance of and a framework for jointly optimizing the human-AI system as opposed to the standard paradigm of optimizing the AI model alone.

We study convergence rates of AdaGrad-Norm as an exemplar of adaptive stochastic gradient methods (SGD), where the step sizes change based on observed stochastic gradients, for minimizing non-convex, smooth objectives. Despite their popularity, the analysis of adaptive SGD lags behind that of non adaptive methods in this setting. Specifically, all prior works rely on some subset of the following assumptions: (i) uniformly-bounded gradient norms, (ii) uniformly-bounded stochastic gradient variance (or even noise support), (iii) conditional independence between the step size and stochastic gradient. In this work, we show that AdaGrad-Norm exhibits an order optimal convergence rate of $\mathcal{O}\left(\frac{\mathrm{poly}\log(T)}{\sqrt{T}}\right)$ after $T$ iterations under the same assumptions as optimally-tuned non adaptive SGD (unbounded gradient norms and affine noise variance scaling), and crucially, without needing any tuning parameters. We thus establish that adaptive gradient methods exhibit order-optimal convergence in much broader regimes than previously understood.

We establish new generalisation bounds for multiclass classification by abstracting to a more general setting of discretised error types. Extending the PAC-Bayes theory, we are hence able to provide fine-grained bounds on performance for multiclass classification, as well as applications to other learning problems including discretisation of regression losses. Tractable training objectives are derived from the bounds. The bounds are uniform over all weightings of the discretised error types and thus can be used to bound weightings not foreseen at training, including the full confusion matrix in the multiclass classification case.

One of the overarching goals of most machine learning algorithms is to generalize to unseen data. Ensuring and quantifying generalization is of course challenging, especially in the high-dimensional setting. One way of reducing the hardness of a learning problem is to study the invariances that may exist with respect to the distribution of data, effectively reducing its dimension. Handling invariances in data has attracted considerable attention over time in machine learning and applied mathematics more broadly. Two notable examples are image registration [De Castro and Morandi, 1987, Reddy and Chatterji, 1996] and time series alignment [Sakoe and Chiba, 1978, Cuturi and Blondel, 2017, Vayer et al., 2020, Blondel et al., 2021, Cohen et al., 2021]. In practice, data augmentation is a central tool in the machine learning practitioner's toolbox. In computer vision for instance, images are randomly cropped, color spaces are changed, artifacts are added.

Vulnerability of various machine learning methods to adversarial examples has been recently explored in the literature. Power systems which use these vulnerable methods face a huge threat against adversarial examples. To this end, we first propose a signal-specific method and a universal signal-agnostic method to attack power systems using generated adversarial examples. Black-box attacks based on transferable characteristics and the above two methods are also proposed and evaluated. We then adopt adversarial training to defend systems against adversarial attacks. Experimental analyses demonstrate that our signal-specific attack method provides less perturbation compared to the FGSM (Fast Gradient Sign Method), and our signal-agnostic attack method can generate perturbations fooling most natural signals with high probability. What's more, the attack method based on the universal signal-agnostic algorithm has a higher transfer rate of black-box attacks than the attack method based on the signal-specific algorithm. In addition, the results show that the proposed adversarial training improves robustness of power systems to adversarial examples. OWER quality refers to a variety of electromagnetic phenomena that characterize voltage and current measured at a given time instance and location in a power system [2]. Disturbance of power quality (PQ) signals can cause severe problems in electrical grids [3].

Existing work (Ji and Grishman, we consider the attention weight between 2008; McClosky et al., 2011; Li et al., 2013; two event mentions as a learned similarity, and we Chen et al., 2015; Du and Cardie, 2020; Li et al., ensure that the attention mechanism learns to align 2021a) traditionally uses a predefined list of event similar events using a semi-supervised contrastive types and their respective annotations to learn an loss. By doing this, we are able to leverage the event extraction model. However, these annotations large variety of semantic information in pretrained are both expensive and time-consuming to language models for clustering unseen types by using create. This problem is amplified when considering a trained attention head. Unlike (Huang and specialization-intensive domains such as scientific Ji, 2020), we are able to separate clustering from literature, which requires years of specialized experience learning, allowing specific task-suited clustering to understand even a specific niche. For algorithms to be selected.