Ancestral graphs are a prevalent mathematical tool to take into account latent (hidden) variables in a probabilistic graphical model.

What types of differences among causal structures with latent variables are impossible to distinguish by statistical data obtained by probing each visible variable? If the probing scheme is simply passive observation, then it is well-known that many different causal structures can realize the same joint probability distributions. Even for the simplest case of two visible variables, for instance, one cannot distinguish between one variable being a causal parent of the other and the two variables sharing a latent common cause. However, it is possible to distinguish between these two causal structures if we have recourse to more powerful probing schemes, such as the possibility of intervening on one of the variables and observing the other. Herein, we address the question of which causal structures remain indistinguishable even given the most informative types of probing schemes on the visible variables. We find that two causal structures remain indistinguishable if and only if they are both associated with the same mDAG structure (as defined by Evans (2016)). We also consider the question of when one causal structure dominates another in the sense that it can realize all of the joint probability distributions that can be realized by the other using a given probing scheme. (Equivalence of causal structures is the special case of mutual dominance.) Finally, we investigate to what extent one can weaken the probing schemes implemented on the visible variables and still have the same discrimination power as a maximally informative probing scheme.

Restricted Boltzmann Machines (RBMs) are widely used probabilistic undirected graphical models with visible and latent nodes, playing an important role in statistics and machine learning. The task of structure learning for RBMs involves inferring the underlying graph by using samples from the visible nodes. Specifically, learning the two-hop neighbors of each visible node allows for the inference of the graph structure. Prior research has addressed the structure learning problem for specific classes of RBMs, namely ferromagnetic and locally consistent RBMs. In this paper, we extend the scope to the quantum computing domain and propose corresponding quantum algorithms for this problem. Our study demonstrates that the proposed quantum algorithms yield a polynomial speedup compared to the classical algorithms for learning the structure of these two classes of RBMs.

The complete learning of an $n$-qubit quantum state requires samples exponentially in $n$. Several works consider subclasses of quantum states that can be learned in polynomial sample complexity such as stabilizer states or high-temperature Gibbs states. Other works consider a weaker sense of learning, such as PAC learning and shadow tomography. In this work, we consider learning states that are close to neural network quantum states, which can efficiently be represented by a graphical model called restricted Boltzmann machines (RBMs). To this end, we exhibit robustness results for efficient provable two-hop neighborhood learning algorithms for ferromagnetic and locally consistent RBMs. We consider the $L_p$-norm as a measure of closeness, including both total variation distance and max-norm distance in the limit. Our results allow certain quantum states to be learned with a sample complexity \textit{exponentially} better than naive tomography. We hence provide new classes of efficiently learnable quantum states and apply new strategies to learn them.

What the heck is it? In Quantum state the parameters like Entropy and temperature impact are observed. Strange thing: It is a model but no output nodes. If you known about ml, simply we have a output and based upon the different learning rule such as gradient descend we learn the values for parameters for weight, and other parameters.(calling it as a learning model) The hidden nodes learn or map the things from given input represented by v in above image. It falls under unsupervised learning as you know it.

The interactive version of this post can be found here. Since Medium does not support Javascript and equations written in Latex, we recommend to check out our interactive post as well. When we think of Peter, his positive nature and his can-do attitude inevitably come to mind. He had an ability to inspire and carry the people around him, convincing them that almost everything is possible. Back in 2018 he came up with the idea for an interactive blog post on the subject of Energy Based Models and pitched it to us. It was almost impossible to resist his enthusiastic manner and of course we embarked on this adventure with him. Equipped with our knowledge in physics and machine learning and hardly any clue about Javascript, we started our journey. After a lot of hard work, we were finally able to complete this project. We are overjoyed with the final result and we wish he could see it.

We study the type of distributions that Restricted Boltzmann Machines (RBMs) with different activation functions can express by investigating the effect of the activation function of the hidden nodes on the marginal distribution they impose on observed binary nodes. We report an exact expression for these marginals in the form of a model of interacting binary variables with the explicit form of the interactions depending on the hidden node activation function. We study the properties of these interactions in detail and evaluate how the accuracy with which the RBM approximates distributions over binary variables depends on the hidden node activation function and on the number of hidden nodes. When the inferred RBM parameters are weak, an intuitive pattern is found for the expression of the interaction terms which reduces substantially the differences across activation functions. We show that the weak parameter approximation is a good approximation for different RBMs trained on the MNIST dataset. Interestingly, in these cases, the mapping reveals that the inferred models are essentially low order interaction models.

Unlike task-specific algorithms, Deep Learning is a part of Machine Learning family based on learning data representations. With massive amounts of computational power, machines can now recognize objects and translate speech in real time, enabling a smart Artificial intelligence in systems. The concept of a software simulating the neocortex's large array of neurons in an artificial neural network is decades old, and it has led to as many disappointments as breakthroughs. But because of improvements in mathematical formulas and increasingly powerful computers, today researchers & data scientists can model many more layers of virtual neurons than ever before. "Recent improvements in Deep Learning has reignited some of the grand challenges in Artificial Intelligence."

In this paper, we propose a biologically-plausible model to explain the emergence of motion tracking behaviour in early development using unsupervised learning. The model's training is biased by a concept called retinal constancy, which measures how similar visual contents are between successive frames. This biasing is similar to a reward in reinforcement learning, but is less explicit, as it modulates the model's learning rate instead of being a learning signal itself. The model is a two-layer deep network. The first layer learns to encode visual motion, and the second layer learns to relate that motion to gaze movements, which it perceives and creates through bi-directional nodes. By randomly generating gaze movements to traverse the local visual space, desirable correlations are developed between visual motion and the appropriate gaze to nullify that motion such that maximal retinal constancy is achieved. Biologically, this is similar to using saccades to look around and learning from moments where a target and the saccade move together such that the image stays the same on the retina, and developing smooth pursuit behaviour to perform this action in the future. Restricted Boltzmann machines are used to implement this model because they can form a deep belief network, perform online learning, and act generatively. These properties all have biological equivalents and coincide with the biological plausibility of using saccades as leverage to learn smooth pursuit. This method is unique because it uses general machine learning algorithms, and their inherent generative properties, to learn from real-world data. It also implements a biological theory, uses motion instead of recognition via local searches, without temporal filtering, and learns in a fully unsupervised manner. Its tracking performance after being trained on real-world images with simulated motion is compared to its tracking performance after being trained on natural video. Results show that this model is able to successfully follow targets in natural video, despite partial occlusions, scale changes, and nonlinear motion.