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Energy Manifold Natural Gradient Descent: From Riemannian Optimization to Modern Neuroscience, NeuroAI and Quantum Physics

Dr. Rishabh Pathak
When Geometry, Energy, Artificial Intelligence and Neuroscience Converge Modern Artificial Intelligence is rapidly moving beyond the idea that learning simply means minimizing an error function. Increasingly, researchers are asking a deeper question: what is the structure of the space in which learning takes place? This question becomes particularly important when the system being modelled is constrained, nonlinear, dynamic, or governed by physical principles. A recent work titled “Energy Manifold Natural Gradient Descent: Riemannian Optimization for Neural PDE Solvers” , by Zhangyong Liang and Huanhuan Gao, introduces Energy Manifold Natural Gradient Descent (EMNGD) , a mathematical framework that extends energy-based natural-gradient optimization from unconstrained Euclidean parameter spaces to constrained Riemannian parameter manifolds . At its core, the framework proposes a simple but powerful principle: An optimization algorithm should not only determine how to reduce error; it sh...
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Haphazard Sampling or Convenience Sampling

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Dr. Rishabh Pathak

Haphazard sampling, also known as convenience sampling, is a non-probability sampling technique where sample units are selected based on their convenient availability to the researcher. This method is characterized by its reliance on easily accessible subjects rather than random selection. Here are some key points about haphazard sampling or convenience sampling:


1.    Definition:

o    Haphazard sampling, or convenience sampling, involves selecting sample units based on their easy accessibility and convenience to the researcher.

o    Researchers choose participants who are readily available or easily reached, without following a systematic or random selection process.

2.    Characteristics:

o    Convenience sampling is a non-probability sampling method that does not involve randomization or known probabilities of selection.

o Sample units are typically chosen based on the researcher's proximity, availability, or ease of access.

3.    Process:

o    In convenience sampling, researchers may select participants who are nearby, willing to participate, or easily reachable through existing networks.

o  This method is often used when time, resources, or logistical constraints make random sampling impractical.

4.    Advantages:

o    Convenience sampling is quick, easy, and cost-effective, making it suitable for exploratory research, pilot studies, or preliminary investigations.

o  This method can be useful for generating initial insights, identifying trends, or exploring research questions in a flexible manner.

5.    Limitations:

o Results obtained from convenience samples may not be representative of the larger population due to selection bias.

o    The lack of randomization in convenience sampling can lead to sampling errors and limit the generalizability of findings.

o    Researchers should be cautious in drawing broad conclusions or making population inferences based on convenience samples.

6.    Applications:

o    Convenience sampling is commonly used in educational research, small-scale studies, qualitative research, and situations where random sampling is impractical.

o    This method is often employed in situations where the focus is on exploring phenomena, generating hypotheses, or gaining initial insights rather than making population estimates.

7.    Considerations:

o Researchers should clearly acknowledge the limitations of convenience sampling in terms of generalizability and potential bias in sample selection.

o  While convenience sampling can be a useful starting point in research, efforts should be made to supplement or validate findings with more rigorous sampling methods when possible.

Convenience sampling, or haphazard sampling, offers a practical and accessible approach to sampling in certain research contexts. While this method provides convenience and flexibility, researchers should be mindful of its limitations in terms of representativeness and potential bias. Careful consideration of the research objectives and constraints is essential when choosing convenience sampling as a sampling strategy.

 

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  1. SRIJune 29, 2024 at 2:59 AM

    Insightful to learn about Research Methods. Thanks for your effort sir (@Dr. Rishabh Pathak)

    ReplyDelete

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