In this article, we will discuss hierarchical clustering algorithms in unsupervised machine learning. This algorithm is based on the splitting and merging of nested clusters. The linkage criteria to merge the clusters based on distance metric as shown below with a bottom-up approach. The linkage criteria give different clusters at different time speeds. Single linkage is not good in noisy data and ward linkage does not give proper cluster because the distance is not varied thus but good in properly balanced clusters and if we do not consider euclidean then average linkage can be used for clustering. The next parameter comes is connectivity that connects or merges the clusters based on the connectivity matrix.

In this article, we will be learning about how we can implement logistic regression by writing Python code. You must be wondering what is logistic regression and what is the theory behind it? What python packages are involved while implementing logistic regression? You must be coming up with many more questions but I will try to answer as many as questions possible. Well, you have chosen the right article.

We propose a new method in which a generative adversarial network (GAN) is used to quantify the uncertainty of forward simulations in the presence of observed data. Previously, a method has been developed which enables GANs to make time series predictions and data assimilation by training a GAN with unconditional simulations of a high-fidelity numerical model. After training, the GAN can be used to predict the evolution of the spatial distribution of the simulation states and observed data is assimilated. In this paper, we describe the process required in order to quantify uncertainty, during which no additional simulations of the high-fidelity numerical model are required. These methods take advantage of the adjoint-like capabilities of generative models and the ability to simulate forwards and backwards in time. Set within a reduced-order model framework for efficiency, we apply these methods to a compartmental model in epidemiology to predict the spread of COVID-19 in an idealised town. The results show that the proposed method can efficiently quantify uncertainty in the presence of measurements using only unconditional simulations of the high-fidelity numerical model.

Deep clustering has the potential to learn a strong representation and hence better clustering performance compared to traditional clustering methods such as $k$-means and spectral clustering. However, this strong representation learning ability may make the clustering unfair by discovering surrogates for protected information which we empirically show in our experiments. In this work, we study a general notion of group-level fairness for both binary and multi-state protected status variables (PSVs). We begin by formulating the group-level fairness problem as an integer linear programming formulation whose totally unimodular constraint matrix means it can be efficiently solved via linear programming. We then show how to inject this solver into a discriminative deep clustering backbone and hence propose a refinement learning algorithm to combine the clustering goal with the fairness objective to learn fair clusters adaptively. Experimental results on real-world datasets demonstrate that our model consistently outperforms state-of-the-art fair clustering algorithms. Our framework shows promising results for novel clustering tasks including flexible fairness constraints, multi-state PSVs and predictive clustering.

EEG is the gold standard for seizure detection in the newborn infant, but EEG interpretation in the preterm group is particularly challenging; trained experts are scarce and the task of interpreting EEG in real-time is arduous. Preterm infants are reported to have a higher incidence of seizures compared to term infants. Preterm EEG morphology differs from that of term infants, which implies that seizure detection algorithms trained on term EEG may not be appropriate. The task of developing preterm specific algorithms becomes extra-challenging given the limited amount of annotated preterm EEG data available. This paper explores novel deep learning (DL) architectures for the task of neonatal seizure detection in preterm infants. The study tests and compares several approaches to address the problem: training on data from full-term infants; training on data from preterm infants; training on age-specific preterm data and transfer learning. The system performance is assessed on a large database of continuous EEG recordings of 575h in duration. It is shown that the accuracy of a validated term-trained EEG seizure detection algorithm, based on a support vector machine classifier, when tested on preterm infants falls well short of the performance achieved for full-term infants. An AUC of 88.3% was obtained when tested on preterm EEG as compared to 96.6% obtained when tested on term EEG. When re-trained on preterm EEG, the performance marginally increases to 89.7%. An alternative DL approach shows a more stable trend when tested on the preterm cohort, starting with an AUC of 93.3% for the term-trained algorithm and reaching 95.0% by transfer learning from the term model using available preterm data.

By producing summaries for long-running events, timeline summarization (TLS) underpins many information retrieval tasks. Successful TLS requires identifying an appropriate set of key dates (the timeline length) to cover. However, doing so is challenging as the right length can change from one topic to another. Existing TLS solutions either rely on an event-agnostic fixed length or an expert-supplied setting. Neither of the strategies is desired for real-life TLS scenarios. A fixed, event-agnostic setting ignores the diversity of events and their development and hence can lead to low-quality TLS. Relying on expert-crafted settings is neither scalable nor sustainable for processing many dynamically changing events. This paper presents a better TLS approach for automatically and dynamically determining the TLS timeline length. We achieve this by employing the established elbow method from the machine learning community to automatically find the minimum number of dates within the time series to generate concise and informative summaries. We applied our approach to four TLS datasets of English and Chinese and compared them against three prior methods. Experimental results show that our approach delivers comparable or even better summaries over state-of-art TLS methods, but it achieves this without expert involvement.

Analysis of large observational data sets generated by a reactive system is a common challenge in debugging system failures and determining their root cause. One of the major problems is that these observational data suffer from survivorship bias. Examples include analyzing traffic logs from networks, and simulation logs from circuit design. In such applications, users want to detect non-spurious correlations from observational data and obtain actionable insights about them. In this paper, we introduce log to Neuro-symbolic (Log2NS), a framework that combines probabilistic analysis from machine learning (ML) techniques on observational data with certainties derived from symbolic reasoning on an underlying formal model. We apply the proposed framework to network traffic debugging by employing the following steps. To detect patterns in network logs, we first generate global embedding vector representations of entities such as IP addresses, ports, and applications. Next, we represent large log flow entries as clusters that make it easier for the user to visualize and detect interesting scenarios that will be further analyzed. To generalize these patterns, Log2NS provides an ability to query from static logs and correlation engines for positive instances, as well as formal reasoning for negative and unseen instances. By combining the strengths of deep learning and symbolic methods, Log2NS provides a very powerful reasoning and debugging tool for log-based data. Empirical evaluations on a real internal data set demonstrate the capabilities of Log2NS.

The reinforcement learning problem of finding a control policy that minimizes the minimum time objective for the Mountain Car environment is considered. Particularly, a class of parameterized nonlinear feedback policies is optimized over to reach the top of the highest mountain peak in minimum time. The optimization is carried out using quasi-Stochastic Gradient Descent (qSGD) methods. In attempting to find the optimal minimum time policy, a new parameterized policy approach is considered that seeks to learn an optimal policy parameter for different regions of the state space, rather than rely on a single macroscopic policy parameter for the entire state space. This partitioned parameterized policy approach is shown to outperform the uniform parameterized policy approach and lead to greater generalization than prior methods, where the Mountain Car became trapped in circular trajectories in the state space.

In this paper, we introduce Target-Aware Weighted Training (TAWT), a weighted training algorithm for cross-task learning based on minimizing a representation-based task distance between the source and target tasks. We show that TAWT is easy to implement, is computationally efficient, requires little hyperparameter tuning, and enjoys non-asymptotic learning-theoretic guarantees. The effectiveness of TAWT is corroborated through extensive experiments with BERT on four sequence tagging tasks in natural language processing (NLP), including part-of-speech (PoS) tagging, chunking, predicate detection, and named entity recognition (NER). As a byproduct, the proposed representation-based task distance allows one to reason in a theoretically principled way about several critical aspects of cross-task learning, such as the choice of the source data and the impact of fine-tuning

Gradient-based methods for two-player games produce rich dynamics that can solve challenging problems, yet can be difficult to stabilize and understand. Part of this complexity originates from the discrete update steps given by simultaneous or alternating gradient descent, which causes each player to drift away from the continuous gradient flow -- a phenomenon we call discretization drift. Using backward error analysis, we derive modified continuous dynamical systems that closely follow the discrete dynamics. These modified dynamics provide an insight into the notorious challenges associated with zero-sum games, including Generative Adversarial Networks. In particular, we identify distinct components of the discretization drift that can alter performance and in some cases destabilize the game. Finally, quantifying discretization drift allows us to identify regularizers that explicitly cancel harmful forms of drift or strengthen beneficial forms of drift, and thus improve performance of GAN training.